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NCERT Solutions for Class 5th Maths Chapter 13 State whether the following statements are true (T) or false (F). — Let Us Do (Question 8: True or False)

Book page 169 Updated on2026-09-19

Q1.
8. (a) Factors of even numbers must be even.
Answer

False (F).

An even number can easily have odd factors.

Factors of 6 → 1, 2, 3, 6  — 1 and 3 are odd
Factors of 10 → 1, 2, 5, 10 — 1 and 5 are odd
Factors of 12 → 1, 2, 3, 4, 6, 12
Why it happens: 6 counters can be set out as 3 rows of 2. The 3 rows make 3 a factor, and 3 is odd. In fact 1 is a factor of every number, and 1 is odd — so no number can have only even factors.
Q2.
8. (b) Multiples of odd numbers cannot be even.
Answer

False (F).

Jump 3 steps at a time and you land on 3, 6, 9, 12, 15, 18 … Every second landing spot is even.

3 × 2 = 6 (even)
3 × 4 = 12 (even)
5 × 2 = 10 (even)
7 × 6 = 42 (even)
Why it happens: An odd number multiplied by an even number always gives an even answer. So the multiples of an odd number go odd, even, odd, even, odd, even … turn by turn.
Check on the number line: The frog jumping 3 lands on 3, 6, 9, 12. Two of those four spots are even.
Q3.
8. (c) Factors of odd numbers cannot be even.
Answer

True (T).

Factors of 9 → 1, 3, 9 — all odd
Factors of 15 → 1, 3, 5, 15 — all odd
Factors of 21 → 1, 3, 7, 21 — all odd
Why it happens: If an even number were a factor of some number, that number could be split into equal groups of 2 — which would make it even. An odd number cannot be split into equal pairs; one is always left over. So no even number can ever divide an odd number exactly.
Try it: Take 15 counters and try to make pairs. You get 7 pairs and 1 counter left over. So 2 is not a factor of 15 — and neither is 4, 6, 8 or any other even number.
Q4.
8. (d) One of the common multiples of two consecutive numbers is their product.
Answer

True (T).

Consecutive numbers are numbers that follow one after the other, like 4 and 5, or 9 and 10.

4 and 5 → 4 × 5 = 20. And 20 ÷ 4 = 5 ✓, 20 ÷ 5 = 4 ✓
9 and 10 → 9 × 10 = 90. And 90 ÷ 9 = 10 ✓, 90 ÷ 10 = 9 ✓
7 and 8 → 7 × 8 = 56 ✓
Why it happens: If you multiply two numbers together, the answer can be split into equal groups of the first number and into equal groups of the second. So the product is always a common multiple — of any two numbers, not only consecutive ones.
Careful: The product is a common multiple, not always the smallest one. For 4 and 6 the product is 24, but the smallest common multiple is 12. For consecutive numbers, though, the product really is the smallest one.
Q5.
8. (e) The only common factor of any two consecutive numbers is 1.
Answer

True (T).

PairFactors of the firstFactors of the secondCommon
8 and 91, 2, 4, 81, 3, 91
12 and 131, 2, 3, 4, 6, 121, 131
14 and 151, 2, 7, 141, 3, 5, 151
Why it happens: Think of jumps again. Suppose a jump of 3 lands on 14. The very next landing spot is 17, not 15 — because after landing, the animal must travel a full 3 steps before it can land again. Two numbers that are only 1 step apart can never both be landing spots for a jump bigger than 1. So the only jump size that reaches both is 1.
Q6.
8. (f) 0 cannot be a factor of any number.
Answer

True (T).

0 × 1 = 0
0 × 5 = 0
0 × 100 = 0

Whatever you multiply 0 by, the answer is always 0
Why it happens: A factor is a number you can multiply by something to get your number. But 0 multiplied by anything gives 0 — never 12, never 25, never any other number. Jumping 0 steps at a time means you never move off 0. So 0 is a factor of no number at all.
Related fact: Dividing by 0 is not allowed in mathematics. You cannot share 12 sweets among 0 children.
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