📘 Class 6 Mathematics – Chapter 5: Prime Time

✨ Complete Notes (All Topics Explained)

1. Factors

Factors হল সেই সংখ্যা, যেগুলো কোনো সংখ্যা কে নিখুঁতভাবে ভাগ করতে পারে।
Example: Factors of 12 → 1, 2, 3, 4, 6, 12

👉 Rules:

1 is a factor of every number.
Every number is a factor of itself.
Factors are always smaller than or equal to the number.

2. Multiples

কোনো সংখ্যাকে 1, 2, 3… দ্বারা গুণ করলে যে সংখ্যাগুলো পাওয়া যায়, সেগুলোই Multiples।
Example: Multiples of 5 → 5, 10, 15, 20, 25…

👉 Rules:

Every number is a multiple of itself.
Multiples are always greater than or equal to the number.
Every multiple is infinite.

3. Prime Numbers

Prime numbers এর কেবল দুটি factor থাকে → 1 এবং সংখ্যাটি নিজেই।
Example: 2, 3, 5, 7, 11

👉 Important:

2 is the only even prime.
Every other prime is odd.
1 is not prime.

4. Composite Numbers

Composite numbers এর 2–এর বেশি factor থাকে।
Example: 4 (factors = 1,2,4), 6 (1,2,3,6)

👉 Note: 1 is neither prime nor composite.

5. Co-prime Numbers

দুটি সংখ্যা যদি 1 ছাড়া অন্য কোনো common factor না থাকে, তাহলে তারা co-prime।
Example: 8 এবং 9 (Factors of 8 → 1,2,4,8; Factors of 9 → 1,3,9; Common factor = 1)

6. Prime Factorisation

কোনো সংখ্যা কে শুধু prime সংখ্যাগুলোর গুণফল আকারে লেখা হলে সেটাই prime factorisation।
Method → Factor Tree
Example:
56 → 2 × 28 → 2 × (2 × 14) → 2 × (2 × (2 × 7))
✅ Answer: 56 = 2 × 2 × 2 × 7

7. HCF (Highest Common Factor)

Common factors এর মধ্যে সবচেয়ে বড় সংখ্যাকে HCF বলে।
Example: Factors of 18 → 1,2,3,6,9,18
Factors of 24 → 1,2,3,4,6,8,12,24
Common factors = 1,2,3,6 → HCF = 6

👉 Methods:

By listing factors
By prime factorisation

8. LCM (Lowest Common Multiple)

Common multiples এর মধ্যে সবচেয়ে ছোট সংখ্যাকে LCM বলে।
Example: Multiples of 6 → 6,12,18,24…
Multiples of 8 → 8,16,24,32…
✅ LCM = 24

👉 Methods:

By listing multiples
By prime factorisation

9. Divisibility Rules

Number	Rule	Example
2	Last digit even	246 ✔
3	Sum of digits multiple of 3	153 ✔
4	Last 2 digits divisible by 4	524 ✔
5	Last digit 0 or 5	425 ✔
6	Divisible by both 2 and 3	132 ✔
7	Double last digit, subtract from rest → result divisible by 7	532 → 53–4=49 ✔
8	Last 3 digits divisible by 8	5160 → 160÷8=20 ✔
9	Sum of digits multiple of 9	234 ✔
10	Last digit 0	560 ✔

10. Tests for Prime Numbers

👉 To check if a number is prime:

Divide it by prime numbers less than or equal to its square root.
Example: Check 97 → √97 ≈ 10 → test by 2,3,5,7 → not divisible → Prime.

11. Difference Between Factors and Multiples

Factors	Multiples
Limited in number	Infinite in number
Smaller or equal to the number	Greater or equal to the number
Example: Factors of 12 = 1,2,3,4,6,12	Multiples of 12 = 12,24,36,48,…

12. Sieve of Eratosthenes (Finding Primes)

Write numbers from 2 to 100.
Circle 2 and cross out all its multiples.
Next uncrossed number (3) → circle it, cross out its multiples.
Continue with 5, 7, 11, … up to √100.
Remaining uncrossed numbers are primes.

13. Important Points to Remember

1 is neither prime nor composite.
2 is the only even prime.
HCF is always a factor, LCM is always a multiple.
Two consecutive numbers are always co-prime.
Every composite number can be expressed as a product of primes.

✨ MCQ Worksheet (25 Questions with Answers)

✅ Multiple Choice Questions (1–25)

Q1. Which is a prime number?
a) 9 b) 11 c) 15 d) 21
👉 Answer: 11 (Factors are only 1 and 11)

Q2. Smallest prime number is –
a) 0 b) 1 c) 2 d) 3
👉 Answer: 2

Q3. Largest prime between 10 and 20 –
a) 17 b) 19 c) 13 d) 11
👉 Answer: 19

Q4. Which is a composite number?
a) 2 b) 3 c) 4 d) 5
👉 Answer: 4 (factors 1,2,4)

Q5. LCM of 4 and 6 =
a) 8 b) 10 c) 12 d) 18
👉 Answer: 12

Q6. HCF of 12 and 18 =
a) 2 b) 4 c) 6 d) 12
👉 Answer: 6

Q7. Co-prime pair is –
a) 12 & 18 b) 9 & 25 c) 14 & 21 d) 20 & 30
👉 Answer: 9 & 25

Q8. Prime factorisation of 30 =
a) 2×3×5 b) 2×15 c) 3×10 d) 5×6
👉 Answer: 2×3×5

Q9. Which number is divisible by 9?
a) 145 b) 279 c) 235 d) 452
👉 Answer: 279 (2+7+9=18, divisible by 9)

Q10. Only even prime number –
a) 1 b) 2 c) 3 d) 4
👉 Answer: 2

Q11. 1 is –
a) Prime b) Composite c) Neither d) Both
👉 Answer: Neither

Q12. LCM of 8 and 12 =
a) 12 b) 24 c) 36 d) 48
👉 Answer: 24

Q13. Prime factors of 84 –
a) 2×2×3×7 b) 2×3×14 c) 3×28 d) 2×42
👉 Answer: 2×2×3×7

Q14. Factors of 45 –
a) 1, 3, 5, 9, 15, 45
b) 1, 2, 3, 6, 9, 18
c) 1, 3, 15, 45
d) 1, 5, 9, 45
👉 Answer: a)

Q15. Which is NOT a prime number?
a) 29 b) 31 c) 33 d) 37
👉 Answer: 33

Q16. LCM of 5 and 15 =
a) 15 b) 30 c) 45 d) 60
👉 Answer: 15

Q17. HCF of 20 and 28 =
a) 2 b) 4 c) 6 d) 8
👉 Answer: 4

Q18. Prime number between 50 and 60 is –
a) 51 b) 53 c) 55 d) 57
👉 Answer: 53

Q19. Which of these is divisible by 11?
a) 231 b) 245 c) 319 d) 451
👉 Answer: 231 (alternating sum 2–3+1=0)

Q20. Which is the smallest composite number?
a) 1 b) 2 c) 3 d) 4
👉 Answer: 4

Q21. Prime factors of 100 =
a) 2×2×5×5 b) 10×10 c) 4×25 d) 20×5
👉 Answer: 2×2×5×5

Q22. Which of these is NOT a co-prime pair?
a) 8 & 9 b) 14 & 15 c) 21 & 22 d) 12 & 20
👉 Answer: 12 & 20 (common factor 4)

Q23. 2-digit largest prime number is –
a) 97 b) 99 c) 89 d) 91
👉 Answer: 97

Q24. LCM of 9 and 12 =
a) 18 b) 24 c) 36 d) 48
👉 Answer: 36

Q25. Which of the following is divisible by 8?
a) 124 b) 256 c) 342 d) 516
👉 Answer: 256 (last three digits 256÷8=32)

✨ True / False Worksheet (25 Questions with Answers)

✅ True / False Questions (1–25)

Q1. 1 is a prime number.
👉 False (It has only one factor)

Q2. 2 is the only even prime number.
👉 True

Q3. Every multiple of 5 ends with 0 or 5.
👉 True

Q4. 49 is a prime number.
👉 False (49 = 7×7)

Q5. Prime factorisation of 100 = 2×2×5×5.
👉 True

Q6. Factors of 18 are 1, 2, 3, 6, 9, 18.
👉 True

Q7. 15 and 28 are co-prime numbers.
👉 True (HCF = 1)

Q8. Every even number greater than 2 is composite.
👉 True

Q9. 3 divides 153 exactly.
👉 True (1+5+3=9, divisible by 3)

Q10. HCF of 8 and 12 is 6.
👉 False (Correct HCF = 4)

Q11. LCM of 6 and 9 is 18.
👉 True

Q12. Every prime is an odd number.
👉 False (2 is an even prime)

Q13. 91 is divisible by 7.
👉 True (7×13=91)

Q14. 125 ends with 5, so divisible by 5.
👉 True

Q15. All composite numbers have more than 2 factors.
👉 True

Q16. 57 is a prime number.
👉 False (57=3×19)

Q17. The smallest composite number is 4.
👉 True

Q18. Multiples of 9 always have a digit sum divisible by 9.
👉 True

Q19. 221 is a prime number.
👉 False (221=13×17)

Q20. 2, 3, 5, 7 are the first four prime numbers.
👉 True

Q21. The number 0 is a multiple of every number.
👉 True

Q22. 81 is divisible by 9.
👉 True (8+1=9)

Q23. 143 is a prime number.
👉 False (143=11×13)

Q24. Every factor of a number is smaller than or equal to the number itself.
👉 True

Q25. Prime factorisation of 36 is 2×2×3×3.
👉 True

✨ Fill in the Blanks Worksheet (25 Questions with Answers)

✅ Fill in the Blanks (1–25)

Q1. Factors of 24 = __________.
👉 Answer: 1, 2, 3, 4, 6, 8, 12, 24

Q2. The smallest prime number is __________.
👉 Answer: 2

Q3. 1 is neither __________ nor __________.
👉 Answer: Prime, Composite

Q4. Multiples of 7 = __________.
👉 Answer: 7, 14, 21, 28, 35 …

Q5. Prime factorisation of 84 = __________.
👉 Answer: 2 × 2 × 3 × 7

Q6. LCM of 5 and 10 = __________.
👉 Answer: 10

Q7. HCF of 12 and 18 = __________.
👉 Answer: 6

Q8. Numbers with only two factors are called __________.
👉 Answer: Prime Numbers

Q9. 2, 3, 5, 7 are __________ numbers.
👉 Answer: Prime

Q10. The sum of digits of 432 is divisible by __________.
👉 Answer: 3 and 9

Q11. Prime factorisation of 36 = __________.
👉 Answer: 2 × 2 × 3 × 3

Q12. Multiples of 9 up to 45 = __________.
👉 Answer: 9, 18, 27, 36, 45

Q13. 2 is the only __________ prime number.
👉 Answer: Even

Q14. 49 is divisible by __________.
👉 Answer: 7

Q15. Numbers like 8 and 9, having only 1 as a common factor, are called __________.
👉 Answer: Co-prime

Q16. The greatest factor of any number is __________.
👉 Answer: The number itself

Q17. The smallest factor of any number is always __________.
👉 Answer: 1

Q18. Prime factorisation of 60 = __________.
👉 Answer: 2 × 2 × 3 × 5

Q19. The LCM of 6 and 8 is __________.
👉 Answer: 24

Q20. The HCF of 16 and 24 is __________.
👉 Answer: 8

Q21. Every multiple of 10 ends with __________.
👉 Answer: 0

Q22. The product of two prime numbers is always a __________ number.
👉 Answer: Composite

Q23. 91 is divisible by __________.
👉 Answer: 7 and 13

Q24. 15 and 28 are __________ numbers.
👉 Answer: Co-prime

Q25. Prime factorisation of 100 = __________.
👉 Answer: 2 × 2 × 5 × 5

✨ Short Answer Worksheet (25 Questions with Step-by-step Answers)

✅ Short Questions with Explained Answers (1–25)

Q1. Find all prime numbers between 10 and 20.
👉 Numbers: 11, 12, 13, 14, 15, 16, 17, 18, 19

11 → Prime
12,14,15,16,18 → Composite
13,17,19 → Prime
✅ Answer: 11, 13, 17, 19

Q2. Write prime factorisation of 90.

90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
✅ Answer: 90 = 2 × 3 × 3 × 5

Q3. Find the smallest number divisible by both 4 and 6.

This means LCM(4,6)
4 = 2 × 2
6 = 2 × 3
LCM = 2 × 2 × 3 = 12
✅ Answer: 12

Q4. Write first 6 multiples of 8.
👉 8 × 1=8, 8×2=16, 8×3=24, 8×4=32, 8×5=40, 8×6=48
✅ Answer: 8, 16, 24, 32, 40, 48

Q5. Find HCF of 24 and 36 by prime factorisation.

24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common factors = 2 × 2 × 3 = 12
✅ Answer: HCF = 12

Q6. Find LCM of 9 and 12 by prime factorisation.

9 = 3 × 3
12 = 2 × 2 × 3
LCM = 2 × 2 × 3 × 3 = 36
✅ Answer: 36

Q7. Are 35 and 64 co-prime?

35 = 5 × 7
64 = 2 × 2 × 2 × 2 × 2 × 2
No common factors except 1
✅ Answer: Yes, 35 and 64 are co-prime

Q8. Write all factors of 45.

Divisors of 45: 1, 3, 5, 9, 15, 45
✅ Answer: 1, 3, 5, 9, 15, 45

Q9. Test divisibility of 252 by 2, 3, 5.

By 2 → last digit 2 → Yes
By 3 → sum = 2+5+2=9 → Yes
By 5 → last digit not 0 or 5 → No
✅ Answer: Divisible by 2 and 3 only

Q10. Write all primes less than 20.
👉 2, 3, 5, 7, 11, 13, 17, 19
✅ Answer: 2, 3, 5, 7, 11, 13, 17, 19

Q11. Write first 5 multiples of 12.
👉 12, 24, 36, 48, 60
✅ Answer: 12, 24, 36, 48, 60

Q12. Write prime factorisation of 120.

120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
✅ Answer: 120 = 2 × 2 × 2 × 3 × 5

Q13. Is 525 divisible by 9?

Sum of digits = 5+2+5=12
12 not divisible by 9
✅ Answer: No

Q14. Find LCM of 8 and 12.

8 = 2 × 2 × 2
12 = 2 × 2 × 3
LCM = 2 × 2 × 2 × 3 = 24
✅ Answer: 24

Q15. Find HCF of 15 and 25.

15 = 3 × 5
25 = 5 × 5
Common = 5
✅ Answer: HCF = 5

Q16. Write first 5 multiples of 7.
👉 7, 14, 21, 28, 35
✅ Answer: 7, 14, 21, 28, 35

Q17. Write prime factorisation of 150.

150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
✅ Answer: 150 = 2 × 3 × 5 × 5

Q18. Find HCF of 20 and 28.

20 = 2 × 2 × 5
28 = 2 × 2 × 7
Common = 2 × 2 = 4
✅ Answer: 4

Q19. Find LCM of 15 and 20.

15 = 3 × 5
20 = 2 × 2 × 5
LCM = 2 × 2 × 3 × 5 = 60
✅ Answer: 60

Q20. Write all prime factors of 210.

210 = 2 × 3 × 5 × 7
✅ Answer: 2, 3, 5, 7

Q21. Check divisibility of 846 by 2, 3, 5, 9.

By 2 → last digit 6 → Yes
By 3 → sum=18 → Yes
By 5 → last digit not 0/5 → No
By 9 → 18 divisible by 9 → Yes
✅ Answer: Divisible by 2, 3, 9

Q22. Find smallest prime factor of 91.

91 ÷ 7 = 13
✅ Answer: 7

Q23. Write first 10 multiples of 6.
👉 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
✅ Answer: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Q24. Write all prime numbers between 30 and 50.
👉 31, 37, 41, 43, 47
✅ Answer: 31, 37, 41, 43, 47

Q25. Find HCF of 32 and 48.

32 = 2^5
48 = 2^4 × 3
Common = 2^4 = 16
✅ Answer: 16

✨ Long Answer Worksheet (25 Questions with Step-by-step Solutions)

✅ Long Questions with Explained Answers (1–25)

Q1. Explain prime, composite and co-prime numbers with examples.
👉

Prime numbers → only 2 factors (e.g., 2, 3, 5).
Composite numbers → more than 2 factors (e.g., 4=2×2, 6=2×3).
Co-prime numbers → HCF = 1 (e.g., 8 and 9).

Q2. Find HCF and LCM of 18 and 24 using prime factorisation.

18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
HCF → common lowest powers = 2 × 3 = 6
LCM → all highest powers = 2×2×2×3×3 = 72
✅ Answer: HCF = 6, LCM = 72

Q3. Explain divisibility rules of 2, 3, 4, 5, 6, 9, 10.
👉

2 → last digit even
3 → sum of digits multiple of 3
4 → last 2 digits divisible by 4
5 → last digit 0 or 5
6 → divisible by 2 and 3
9 → sum of digits multiple of 9
10 → last digit 0

Q4. Use factor tree to find prime factors of 120.

120 = 12 × 10
12 = 3 × 4 = 3 × (2 × 2)
10 = 2 × 5
✅ Prime factors: 120 = 2 × 2 × 2 × 3 × 5

Q5. Check divisibility of 735 by 2, 3, 5, 7, 9, 11.

By 2 → last digit 5 → No
By 3 → sum=15 → Yes
By 5 → last digit 5 → Yes
By 7 → 73–(2×5)=63 → divisible → Yes
By 9 → 15 not divisible → No
By 11 → (7–3+5)=9 → No
✅ Answer: Divisible by 3, 5, 7

Q6. Find smallest number divisible by 15, 20 and 25.

Prime factors:
- 15=3×5
- 20=2^2×5
- 25=5^2
LCM = 2^2 × 3 × 5^2 = 300
✅ Answer: 300

Q7. Write first 10 multiples of 12 and find common multiples with 8.

Multiples of 12: 12,24,36,48,60,72,84,96,108,120
Multiples of 8: 8,16,24,32,40,48,56,64,72,80,88,96
Common: 24,48,72,96
✅ Answer: 24, 48, 72, 96

Q8. Find HCF of 20, 28 and 36.

20=2×2×5
28=2×2×7
36=2×2×3×3
Common = 2×2=4
✅ Answer: 4

Q9. Find LCM of 8, 9 and 12.

8=2^3
9=3^2
12=2^2×3
LCM = 2^3 × 3^2 = 72
✅ Answer: 72

Q10. Prove that 97 is a prime number.

Check divisibility by primes ≤ √97≈10 (2,3,5,7).
97 not divisible by 2,3,5,7.
✅ Answer: 97 is prime

Q11. Explain why 1 is neither prime nor composite.

Prime → needs 2 factors.
Composite → needs more than 2 factors.
1 has only 1 factor (itself).
✅ Answer: Neither prime nor composite

Q12. Show that product of two prime numbers is always composite.

Example: 2×3=6 (factors: 1,2,3,6)
More than 2 factors → composite.
✅ Answer: True

Q13. Find prime factors of 210.

210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
✅ Answer: 210 = 2 × 3 × 5 × 7

Q14. Show that 13 × 17 is composite.

13 and 17 are prime
Their product = 221
221 has factors 1,13,17,221 → composite
✅ Answer: 221 is composite

Q15. Explain difference between factors and multiples with examples.

Factors → divide number exactly (12 → 1,2,3,4,6,12)
Multiples → results of multiplication (12 → 12,24,36,48,…)

Q16. Write all prime numbers between 30 and 50.

31, 37, 41, 43, 47
✅ Answer: 31, 37, 41, 43, 47

Q17. Find LCM of 18, 24 and 30.

18=2×3^2
24=2^3×3
30=2×3×5
LCM = 2^3 × 3^2 × 5 = 360
✅ Answer: 360

Q18. Find HCF of 48 and 60.

48=2^4×3
60=2^2×3×5
HCF = 2^2×3 = 12
✅ Answer: 12

Q19. Check divisibility of 1001 by 7, 11 and 13.

1001 ÷ 7 = 143
143 ÷ 11 = 13
✅ Answer: 1001 = 7 × 11 × 13

Q20. Write first 15 multiples of 5.
👉 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75

Q21. Find prime factorisation of 96 using factor tree.

96=2×48
48=2×24
24=2×12
12=2×6
6=2×3
✅ Answer: 96=2^5×3

Q22. Explain Sieve of Eratosthenes method of finding primes up to 100.

Write numbers 2 to 100
Circle 2, cross multiples
Next uncrossed (3) → circle, cross multiples
Continue with 5,7,11… up to √100
Remaining uncrossed = primes

Q23. Find LCM of 14, 21 and 36.

14=2×7
21=3×7
36=2^2×3^2
LCM=2^2×3^2×7=252
✅ Answer: 252

Q24. Find HCF of 63, 84 and 105.

63=3^2×7
84=2^2×3×7
105=3×5×7
Common=3×7=21
✅ Answer: 21

Q25. Write first 20 prime numbers.
👉 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71

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Prime Time – NCERT Class 6 Mathematics Chapter 5 Notes, Summary, Questions Answers & Worksheet