**Answer:**

1. Answer: (a) 10 × 5 + 2

**Explanation:** 52 = 50+2

=(10×5)+(2×1)

=10×5+2

2. Answer: (a) 10 × 3 + 9

**Explanation:** 39 = 30+9

=(10×3)+(9×1)

=10×3+9

3. Answer: (b) 333

**Explanation: **The general form of any three-digit number is, abc =a×100+b×10+c

Here, 3×100+3×10+3

=300+30+3

=333

4. Answer: (a) 718

**Explanation:**100 x 7 + 10 x 1 + 8

= 700 + 10 + 8

= 718

5. Answer: (d) 50

**Explanation:** In 19, 27, 99, one’s digit is not divisible by 2.

6. Answer: (c) 500

**Explanation: **In 500, one’s digit is divisible by 2.

7. Answer: (b) 37

**Explanation:** In 37, one’s digit is not divisible by 2.

8. Answer: (a) 0 or 3 or 6 or 9

**Explanation: **1 + 0 + 8 = 9

1 + 3 + 8 = 12;

9, 12, 15, 18 each is divisible by 3

9. Answer: (b) 3

**Explanation:** 9 + 2 + 7 = 18

9 + 5 + 7 = 21;

9 + 8 + 7 = 24.

each of 18, 21 and 24 is divisible by 3

10. Answer: (a) 1

**Explanation:** Since the number 21y5 is a multiple of 9.

So, the sum of its digits 2+1+y+5=8+y is a multiple of 9.

∴(8+y) is either 0 or 9 or 18 or ...

Since y is a digit, so (8+y) must be equal to 9.

i.e., 8+y=9

⇒ y=9−8

=1

11. Answer: (d) 457

**Explanation:** 4 + 5 + 7 = 16 is not divisible by 3.

12. Answer: (b) 237

**Explanation:** 2 + 3 + 7 = 12 is divisible by 3.

13. Answer: (a) 234

**Explanation: **2 + 3 + 4 = 9 is divisible by 9.

14. Answer: (c) 122

**Explanation:** To be completely divisible by 5, the number should have 0 or 5 at its one’s digit place.

15. Answer: (c) 110

**Explanation:** If any number has 0 at its one’s digit place, then it is divisible by 10.

Hence, 110/10 = 11

16. Answer: (b) 3

**Explanation:** A number is divisible by 9 if the sum of the digits of the number is divisible by 9.

Sum of digits of given number =2+4+x

= 6+x

Let us say that (x+6) is a multiple of 9,

⟹ x + 6 = 9

x=3

17. Answer: (b) 3

**Explanation: **2146587 = 2 + 1 + 4 + 6 + 5 + 8 + 7 = 33

Since 33 is divisible by 3, hence 2146587 is divisible by 3

18. Answer: (b) 90

**Explanation: **At the unit place of 90 we have 0. Hence, as per the divisibility rule for 5, 90 is divisible by 5.

19. Answer: (a) 1

**Explanation: **Given, 80x is divisible by 9.

Thus, sum of digits of 80x will also be divisible by 9.

8 + 0 + x is divisible by 9 only if, x = 1

8 + 0 + 1

= 9

20. Answer: (b) Either 3 or 8

**Explanation:** N divided by 5 leaves a remainder of 3

→ We know, A number divisible by 5 has Unit Digit 0 or 5.

⇒ Unit Digit of N=0+3=3 or 5+3=8

21. Answer: (b) 79968

**Explanation:** Divisibility rule of 12: Number divisible by both 3 and 4.

⇒ Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3.

⇒ Divisibility rule of 4: A number is divisible by 4 if the last two digits are a multiple of 4.

⇒ 123452=1+2+3+4+5+2=17

⇒ 78968=7+8+9+6+8=28

⇒ 123452 and 78968 are not divisible by 3 so it's not divisible by 12

⇒ 79998=7+9+9+9+8=42, it is divisible by 3.

⇒ Last two digits 98 is not divisible by 4

∴ 79998 is not divisible by 12.

⇒ 79968=7+9+9+6+8=39, it is divisible by 3

⇒ Last two digits 68 are divisible by 4.

∴ 79968 is divisible by 12.

22. Answer: (c) 6

**Explanation:** Factors of 477=1,3,9,53,159,477

The number 477 is divisible by each of the following numbers except 6.

23. Answer: (b) 3

**Explanation:** If N/5 gives remainder 3, then N = 5a+3 for a natural number a.For a being even, 5a has unit place 0 and 3 added gives unit place 3 For a being odd, 5a has unit place 5 and 3 added gives unit place 8. So, it's either 3 or 8.

24. Answer: (a) True

**Explanation:** A number divisible by 8 will be divisible by 4 as 4 is a factor of 8 (Example: 24 is divisible by both 4 and 8), but vice versa may not be true (Example: 20 is divisible by 4 but not by 8). So, the answer is True.

25. Answer: (d) 91

**Explanation:** 91 is divisible by 7 and 13. So, it is not a prime number.

Rest all the given numbers are prime numbers since they don't have any factors other than 1 and themselves.

**Click here** Practice MCQ Question for Playing with Numbers Class 8