NCERT Solutions for Class 5th Maths Chapter 13 Which numbers do jumps of 4 reach? Common factors of number pairs — Let Us Do (Questions 6–7)
Book page 169 Updated on2026-09-19
Q1.
6. Find which of the following numbers can be reached by jumps of 4 steps?Page 169, Question 6 — the number line with 0, 10, 16, 27, 36 and 48 marked on it.
4 is the common factor of the numbers ____________.
Answer
Jumps of 4 reach 16, 36 and 48. They do not reach 10 or 27.
4 is the common factor of the numbers 16, 36 and 48.
The red dots are the landing spots for jumps of 4. They fall on 16, 36 and 48, but skip past 10 and 27.
Number
Divide by 4
Reached?
10
10 ÷ 4 = 2 with 2 left over
No
16
16 ÷ 4 = 4 exactly
Yes
27
27 ÷ 4 = 6 with 3 left over
No
36
36 ÷ 4 = 9 exactly
Yes
48
48 ÷ 4 = 12 exactly
Yes
Why it happens: A 4-jump lands on 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 — the 4 times table. 10 sits between 8 and 12, and 27 sits between 24 and 28, so the jumps go straight over them. Also, 27 is an odd number, and a 4-jump can never land on an odd number.
Q2.
7. (a) 12 and 16
Answer
The common factors of 12 and 16 are 1, 2, 4.
Factors of 12
1, 2, 3, 4, 6, 12
Factors of 16
1, 2, 4, 8, 16
Common factors
1, 2, 4
Write every factor of 12.
Write every factor of 16.
Pick the numbers that are in both lists. They are 1, 2, 4.
Why it happens: Both numbers are built from 4s: 12 = 4 × 3 and 16 = 4 × 4. So 4 divides both, and so do 4's own factors, 1 and 2. But 3 divides only 12, and 8 divides only 16.
Q3.
7. (b) 8 and 12
Answer
The common factors of 8 and 12 are 1, 2, 4.
Factors of 8
1, 2, 4, 8
Factors of 12
1, 2, 3, 4, 6, 12
Common factors
1, 2, 4
Write every factor of 8.
Write every factor of 12.
Pick the numbers that are in both lists. They are 1, 2, 4.
Why it happens: 8 = 4 × 2 and 12 = 4 × 3. So 4 is the biggest common factor, and the common factors are exactly the factors of 4 — that is 1, 2 and 4.
Q4.
7. (c) 4 and 16
Answer
The common factors of 4 and 16 are 1, 2, 4.
Factors of 4
1, 2, 4
Factors of 16
1, 2, 4, 8, 16
Common factors
1, 2, 4
Write every factor of 4.
Write every factor of 16.
Pick the numbers that are in both lists. They are 1, 2, 4.
Why it happens: 4 is itself a factor of 16, because 16 = 4 × 4. When the smaller number divides the bigger one, the common factors are simply all the factors of the smaller number.
Q5.
7. (d) 2 and 9
Answer
The common factors of 2 and 9 are 1.
Factors of 2
1, 2
Factors of 9
1, 3, 9
Common factors
1
Write every factor of 2.
Write every factor of 9.
Pick the numbers that are in both lists. They are 1.
Why it happens: 2 is even and 9 is odd, so 2 cannot divide 9. And 9's other factors, 3 and 9, are too big to divide 2. Only 1 is left.
Notice: When 1 is the only common factor, the two numbers share nothing else at all.
Q6.
7. (e) 3 and 5
Answer
The common factors of 3 and 5 are 1.
Factors of 3
1, 3
Factors of 5
1, 5
Common factors
1
Write every factor of 3.
Write every factor of 5.
Pick the numbers that are in both lists. They are 1.
Why it happens: 3 and 5 are both prime numbers — each has only two factors, itself and 1. Since 3 does not divide 5, the only number they share is 1.
Q7.
7. (f) 12 and 15
Answer
The common factors of 12 and 15 are 1, 3.
Factors of 12
1, 2, 3, 4, 6, 12
Factors of 15
1, 3, 5, 15
Common factors
1, 3
Write every factor of 12.
Write every factor of 15.
Pick the numbers that are in both lists. They are 1, 3.
Why it happens: Both numbers are in the 3 times table: 12 = 3 × 4 and 15 = 3 × 5. So 3 is a common factor. But 12 is even and 15 is odd, so 2 is not.
Q8.
7. (f) 20 and 5
Answer
The common factors of 20 and 5 are 1, 5.
Factors of 20
1, 2, 4, 5, 10, 20
Factors of 5
1, 5
Common factors
1, 5
Write every factor of 20.
Write every factor of 5.
Pick the numbers that are in both lists. They are 1, 5.
Why it happens: 5 divides 20 exactly, because 20 = 5 × 4. So the common factors are all the factors of 5, which are 1 and 5.
A note on the book: This list also prints the label (f) twice — once for "12 and 15" and again for "20 and 5". There are nine pairs in all, and all nine are answered here in the printed order.
Q9.
7. (g) 9 and 21
Answer
The common factors of 9 and 21 are 1, 3.
Factors of 9
1, 3, 9
Factors of 21
1, 3, 7, 21
Common factors
1, 3
Write every factor of 9.
Write every factor of 21.
Pick the numbers that are in both lists. They are 1, 3.
Why it happens: 9 = 3 × 3 and 21 = 3 × 7. The only number they both contain is 3, so the common factors are 1 and 3.
Q10.
7. (h) 6 and 27
Answer
The common factors of 6 and 27 are 1, 3.
Factors of 6
1, 2, 3, 6
Factors of 27
1, 3, 9, 27
Common factors
1, 3
Write every factor of 6.
Write every factor of 27.
Pick the numbers that are in both lists. They are 1, 3.
Why it happens: 6 = 3 × 2 and 27 = 3 × 9. They share the 3. But 6 is even and 27 is odd, so 2 is not shared.
Q11.
What do you notice about the common factors of different pairs of numbers. Discuss in class.
Answer
Sample answer: Every pair of numbers has at least one common factor — the number 1. Some pairs have nothing else. The list of common factors is always short, and it always stops; it can never go past the smaller of the two numbers.
Kind of pair
Examples from this exercise
Common factors
The smaller number divides the bigger one
4 and 16; 20 and 5
All the factors of the smaller number
They share a factor bigger than 1
12 and 16; 12 and 15; 9 and 21; 6 and 27
1 and that shared factor (and its factors)
They share nothing but 1
2 and 9; 3 and 5
Only 1
Four things to notice:
1 is a common factor of every pair. A jump of 1 lands on every number.
The list of common factors always ends — unlike common multiples, which go on for ever.
No common factor is bigger than the smaller number. For 9 and 21, nothing above 9 can be a common factor.
The whole list is made of the factors of the biggest common factor. For 12 and 16 the biggest is 4, and the list 1, 2, 4 is exactly the factors of 4.
Why it happens: A common factor has to fit inside both numbers. The smaller number sets the limit, because nothing larger than a number can divide it.