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NCERT Solutions for Class 5th Maths Chapter 13 Jumps of 2, 3, 5 and 10 along the trail — Mowgli's Jumps and Common Factors

Book page 168 Updated on2026-09-19

Q1.
Did Mowgli meet the ant, frog, bird and the rabbit? Notice their positions— 4, 12, 14, and 50. 2 is a common factor of these numbers.
Answer

Yes, he met all four of them. Their houses stand on 4, 12, 14 and 50, and every one of those numbers is even.

4 ÷ 2 = 2, nothing left over
12 ÷ 2 = 6, nothing left over
14 ÷ 2 = 7, nothing left over
50 ÷ 2 = 25, nothing left over

So 2 is a common factor of 4, 12, 14 and 50
Why it happens: A common factor of some numbers is a number that divides every one of them exactly. Here the jump size is 2, and 2 goes into 4, 12, 14 and 50 with nothing left over — which is exactly why Mowgli's 2-jumps land on all four houses.
Say it the other way round: 4, 12, 14 and 50 are all multiples of 2. Factor and multiple are the same fact seen from two ends: 2 is the jump, and 4, 12, 14, 50 are the landing spots.
Q2.
Which of his friends will he be able to meet if he jumps by 3 steps? (3 is a common factor of the numbers 9, 21, 39, and 57.)
Answer

With jumps of 3 he meets the spider at 9, the frog at 12, Kaa at 21, Baloo at 30, the deer at 39 and the monkey at 57.

0Mowgli4Ant9Spider12Frog14Bird21Kaa26Tiger30Baloo35Akela39Deer50Rabbit57MonkeyGreen = Mowgli lands here (jumps of 3) · Grey = he jumps over
Jumping 3 at a time, Mowgli lands on 3, 6, 9, 12 … 57 — the multiples of 3.
  1. Write where 3-jumps land. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57.
  2. Look up each friend's number in that list.
  3. Keep the ones you find. 9, 12, 21, 30, 39 and 57 are all there.
9 = 3 × 3 ✓
12 = 3 × 4 ✓
21 = 3 × 7 ✓
30 = 3 × 10 ✓
39 = 3 × 13 ✓
57 = 3 × 19 ✓
Why it happens: A 3-jump can only stop on a multiple of 3. To test a number quickly, add up its digits: if the total is in the 3 times table, the number is too. For 57, 5 + 7 = 12, and 12 is a multiple of 3 — so 57 is as well.
What your book prints: The book names four of them — 9, 21, 39 and 57 — and says 3 is a common factor of those numbers. That is true. But 12 and 30 are multiples of 3 as well, so the frog and Baloo are also met.
Q3.
Which numbers will he touch if he jumps by 5 steps? 5 is a common factor of the numbers ____________.
Answer

He touches 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55. Among his friends he meets Baloo at 30, Akela at 35 and the rabbit at 50.

So the blank is filled like this:

5 is a common factor of the numbers 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55.
0Mowgli4Ant9Spider12Frog14Bird21Kaa26Tiger30Baloo35Akela39Deer50Rabbit57MonkeyGreen = Mowgli lands here (jumps of 5) · Grey = he jumps over
Jumps of 5 land only on numbers ending in 5 or 0.
Why it happens: Adding 5 again and again gives 5, 10, 15, 20 … Every one of these ends in a 5 or a 0. So a number can be reached by 5-jumps only if its last digit is 5 or 0. Baloo's 30 ends in 0 ✓, Akela's 35 ends in 5 ✓, the rabbit's 50 ends in 0 ✓.
Check it yourself: 5 × 6 = 30, 5 × 7 = 35, 5 × 10 = 50. All three friends are reached ✓
Q4.
Which numbers will he touch if he jumps by 10 steps? 10 is a common factor of the numbers ____________.
Answer

He touches 10, 20, 30, 40 and 50. Among his friends he meets only Baloo at 30 and the rabbit at 50.

10 is a common factor of the numbers 10, 20, 30, 40 and 50.
0Mowgli4Ant9Spider12Frog14Bird21Kaa26Tiger30Baloo35Akela39Deer50Rabbit57MonkeyGreen = Mowgli lands here (jumps of 10) · Grey = he jumps over
Jumps of 10 land only on numbers ending in 0.
Why it happens: Adding 10 each time only changes the tens digit. The ones digit stays 0. So a 10-jump can land only on a number ending in 0 — 10, 20, 30, 40, 50.
Notice the pattern: Every number reached by 10-jumps is also reached by 5-jumps and by 2-jumps. That is because 10 = 2 × 5, so 2 and 5 are both factors of 10.
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