NCERT Solutions for Class 5th Maths Chapter 13 Common factors of 24 and 36; common factors of 12 and 13 — Let Us Do (Questions 4–5)
Book page 168 Updated on2026-09-19
Q1.
4. (a) Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No. 2 is/is not a common factor of 24 and 36.
Answer
Yes. 2 is a common factor of 24 and 36.
Jumping 2 at a time from 0, you land on both 24 and 36.
24 ÷ 2 = 12, nothing left over ✓ 36 ÷ 2 = 18, nothing left over ✓
So 2 is a common factor of 24 and 36
Why it happens: Both 24 and 36 are even numbers, so both can be shared into equal pairs. That is the same as saying 2 divides each of them exactly.
Q2.
4. (b) Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No. 3 is/is not a common factor of 24 and 36.
Answer
Yes. 3 is a common factor of 24 and 36.
Jumping 3 at a time, you land on 3, 6, 9 … 24 … 36. Both targets are hit.
24 ÷ 3 = 8, nothing left over ✓ 36 ÷ 3 = 12, nothing left over ✓
Why it happens: Add the digits and check. For 24, 2 + 4 = 6, and 6 is in the 3 times table. For 36, 3 + 6 = 9, also in the 3 times table. So 3 divides both.
Q3.
4. (c) Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No. 4 is/is not a common factor of 24 and 36.
Answer
Yes. 4 is a common factor of 24 and 36.
Jumping 4 at a time: 4, 8, 12, 16, 20, 24, 28, 32, 36. Both 24 and 36 are landing spots.
24 ÷ 4 = 6, nothing left over ✓ 36 ÷ 4 = 9, nothing left over ✓
Why it happens: 4 × 6 = 24 and 4 × 9 = 36. Because both numbers can be built out of equal groups of 4, a 4-jump lands exactly on each of them.
Q4.
4. (d) What other jumps can we take to reach both 24 and 36?
Answer
Jumps of 1, 6 and 12 also reach both numbers.
Three more jump sizes that land on both 24 and 36.
Jump of 1: 24 ÷ 1 = 24 ✓ and 36 ÷ 1 = 36 ✓ Jump of 6: 24 ÷ 6 = 4 ✓ and 36 ÷ 6 = 6 ✓ Jump of 12: 24 ÷ 12 = 2 ✓ and 36 ÷ 12 = 3 ✓
Some jump sizes do not work:
Jump of 5: 24 ÷ 5 leaves 4 over ✗ Jump of 8: 36 ÷ 8 leaves 4 over ✗ Jump of 9: 24 ÷ 9 leaves 6 over ✗
Why it happens: A jump size works only if it divides both numbers exactly. 8 divides 24 but not 36, so it is a factor of 24 alone — not a common factor.
Q5.
4. (e) How many common factors can you find for 24 and 36? List them.
Answer
There are six common factors: 1, 2, 3, 4, 6 and 12.
List all the factors of 24. 1, 2, 3, 4, 6, 8, 12, 24.
List all the factors of 36. 1, 2, 3, 4, 6, 9, 12, 18, 36.
Tick the numbers that are in both lists. 1, 2, 3, 4, 6, 12.
Count them. Six common factors.
Factors of 24
1, 2, 3, 4, 6, 8, 12, 24
Factors of 36
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors
1, 2, 3, 4, 6, 12
Why it happens: Unlike common multiples, common factors always run out. No common factor can be bigger than the smaller number, so for 24 and 36 the search stops at 24. Here the biggest common factor is 12.
Notice: The common factors 1, 2, 3, 4, 6 and 12 are exactly the factors of 12 — the biggest common factor. That happens with every pair of numbers.
Q6.
4. (f) What about jumping by 1 step each time to reach both 24 and 36?
Answer
Yes, a jump of 1 works — and it works for every number.
Jumping 1 at a time: 1, 2, 3, 4, 5 … 24 … 36 24 ÷ 1 = 24 ✓ and 36 ÷ 1 = 36 ✓
Why it happens: Jumping 1 step at a time means you touch every number on the number line. So you must pass through 24 and through 36. This is why 1 is a common factor of every pair of numbers.
The book's note says:The number itself and 1 are always factors of any number. So the shortest list of common factors any two numbers can have is just 1.
Q7.
5. What are the common factors of 12 and 13?
Answer
The only common factor of 12 and 13 is 1.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 13: 1, 13 — because 13 is a prime number.
Compare the two lists. The only number in both is 1.
Factors of 12 → 1, 2, 3, 4, 6, 12 Factors of 13 → 1, 13
Common factor = 1
Why it happens: 13 has only two factors, 1 and 13. Since 13 does not divide 12 (12 ÷ 13 is not a whole number), the only factor they can share is 1.
Did you know? 12 and 13 follow one another on the number line. Two numbers that follow one another always have 1 as their only common factor.