NCERT Solutions for Class 5th Maths Chapter 13 Make different arrays for the following numbers. Identify the factors in each case. — Let Us Do
Book page 165 Updated on2026-09-19
Q1.
(a) 10
Answer
Factors of 10: 1, 2, 5, 10. That is 4 factors in all.
Arrays for 10. Each rectangle gives a pair of factors.
1 × 10 = 10 → factors 1 and 10 2 × 5 = 10 → factors 2 and 5
All the factors of 10 = 1, 2, 5, 10
Why it happens: 10 counters can be set out as one row of 10, or as 2 rows of 5. They cannot be set out as 3 equal rows or 4 equal rows, so 3 and 4 are not factors of 10.
Check it yourself: 2 × 5 = 10 and 1 × 10 = 10. Multiply each pair — both give 10 ✓
Q2.
(b) 14
Answer
Factors of 14: 1, 2, 7, 14. That is 4 factors in all.
Arrays for 14. Each rectangle gives a pair of factors.
1 × 14 = 14 → factors 1 and 14 2 × 7 = 14 → factors 2 and 7
All the factors of 14 = 1, 2, 7, 14
Why it happens: 14 is even, so it splits into 2 equal rows of 7. After that nothing else works — 3, 4, 5 and 6 all leave counters over.
Q3.
(c) 13
Answer
Factors of 13: 1, 13. That is 2 factors in all.
Only one rectangle is possible for 13 — a single row.
1 × 13 = 13 → factors 1 and 13
All the factors of 13 = 1, 13
Why it happens: 13 counters can only be laid out as one single row. Try 2 rows — you get 6 and 7, which are not equal. Try 3 rows, 4 rows, 5 rows, 6 rows — every time some counters are left over. So 13 has only two factors.
Did you know? A number with exactly two factors, 1 and itself, is called a prime number. 13 is prime.
Q4.
(d) 20
Answer
Factors of 20: 1, 2, 4, 5, 10, 20. That is 6 factors in all.
Arrays for 20. Each rectangle gives a pair of factors.
1 × 20 = 20 → factors 1 and 20 2 × 10 = 20 → factors 2 and 10 4 × 5 = 20 → factors 4 and 5
All the factors of 20 = 1, 2, 4, 5, 10, 20
Why it happens: Test the numbers one by one. 20 ÷ 1 = 20 ✓, 20 ÷ 2 = 10 ✓, 20 ÷ 3 leaves 2 over ✗, 20 ÷ 4 = 5 ✓, 20 ÷ 5 = 4 ✓. After 4 × 5 the pairs start repeating, so you can stop.
Q5.
(e) 25
Answer
Factors of 25: 1, 5, 25. That is 3 factors in all.
25 counters make a perfect square: 5 rows of 5.
1 × 25 = 25 → factors 1 and 25 5 × 5 = 25 → factors 5 and 5
All the factors of 25 = 1, 5, 25
The other rectangle is one row of 25 counters, which gives the factors 1 and 25.
Why it happens: 25 makes a perfect square — 5 rows of 5. When a number makes a square array, the two factors in that pair are the same number, so it gets counted only once. That is why 25 has an odd number of factors: three.
Try This: Which other numbers make a perfect square array? 4 (2 × 2), 9 (3 × 3), 16 (4 × 4), 36 (6 × 6).
Q6.
(f) 32
Answer
Factors of 32: 1, 2, 4, 8, 16, 32. That is 6 factors in all.
Arrays for 32. Each rectangle gives a pair of factors.
1 × 32 = 32 → factors 1 and 32 2 × 16 = 32 → factors 2 and 16 4 × 8 = 32 → factors 4 and 8
All the factors of 32 = 1, 2, 4, 8, 16, 32
Why it happens: 32 keeps halving: 32, 16, 8, 4, 2, 1. Every one of those is a factor. No odd number except 1 divides 32, because 32 is made only of 2s: 2 × 2 × 2 × 2 × 2 = 32.
Q7.
(g) 37
Answer
Factors of 37: 1, 37. That is 2 factors in all.
37 counters make only one rectangle — a single long row.
1 × 37 = 37 → factors 1 and 37
All the factors of 37 = 1, 37
Why it happens: Try 2 rows, 3 rows, 4 rows, 5 rows, 6 rows — every single time some counters are left over. Only one long row works.
Did you know? 37 is a prime number, just like 13.
Q8.
(h) 46
Answer
Factors of 46: 1, 2, 23, 46. That is 4 factors in all.
46 counters as 2 rows of 23. The other rectangle is one row of 46.
1 × 46 = 46 → factors 1 and 46 2 × 23 = 46 → factors 2 and 23
All the factors of 46 = 1, 2, 23, 46
Why it happens: 46 is even, so 2 rows of 23 work. After that, 3, 4, 5 … up to 22 all leave counters over, because 23 is itself a prime number.
Q9.
(i) 54
Answer
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. That is 8 factors in all.
Arrays for 54. Each rectangle gives a pair of factors.
1 × 54 = 54 → factors 1 and 54 2 × 27 = 54 → factors 2 and 27 3 × 18 = 54 → factors 3 and 18 6 × 9 = 54 → factors 6 and 9
All the factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Why it happens: 54 is even, so 2 is a factor. 5 + 4 = 9, and 9 is in the 3 times table, so 3 is a factor too. Working through the pairs gives 1 × 54, 2 × 27, 3 × 18 and 6 × 9 — eight factors in all.
Check it yourself: 6 × 9 = 54 ✓ and 3 × 18 = 54 ✓
Q10.
Numbers like 13 and 37 are called prime numbers. Why?
Answer
Because 13 and 37 have exactly two factors each — 1 and the number itself. Nothing else divides them.
You can see it in the arrays. Most numbers make more than one rectangle. 13 and 37 make only one: a single long row.
Number
Rectangles you can make
Factors
Prime?
10
1 × 10, 2 × 5
1, 2, 5, 10
No — four factors
13
1 × 13 only
1, 13
Yes
14
1 × 14, 2 × 7
1, 2, 7, 14
No
37
1 × 37 only
1, 37
Yes
Why it happens: To check whether 13 is prime, try to share 13 counters into equal groups. Groups of 2 leave 1 over. Groups of 3 leave 1 over. Groups of 4, 5 and 6 all leave some over. Since nothing between 2 and 12 divides 13, the only factors left are 1 and 13.
Tip: The prime numbers below 40 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37. Notice that 1 is not prime — it has only one factor, not two.