Playing with Numbers Ex 3.1
(a) 24
(b) 15
(c) 21
(d) 27
(e) 12
(f) 20
(g) 18
(h) 23
(i) 36
Solutions:
(a) 24
24 = 1 × 24
24 = 2 × 12
24 = 3 × 8
24 = 4 × 6
24 = 6 × 4
Hence, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
(b) 15
15 = 1 × 15
15 = 3 × 5
15 = 5 × 3
Hence, the factors of 15 are 1, 3, 5 and 15
(c) 21
21 = 1 × 21
21 = 3 × 7
21 = 7 × 3
Hence, the factors of 21 are 1, 3, 7 and 21
(d) 27
27 = 1 × 27
27 = 3 × 9
27 = 9 × 3
Hence, the factors of 27 are 1, 3, 9 and 27
(e) 12
12 = 1 × 12
12 = 2 × 6
12 = 3 × 4
12 = 4 × 3
Hence, the factors of 12 are 1, 2, 3, 4, 6 and 12
(f) 20
20 = 1 × 20
20 = 2 × 10
20 = 4 × 5
20 = 5 × 4
Hence, the factors of 20 are 1, 2, 4, 5 10 and 20
(g) 18
18 = 1 × 18
18 = 2 × 9
18 = 3 × 6
18 = 6 × 3
Hence, the factors of 18 are 1, 2, 3, 6, 9 and 18
(h) 23
23 = 1 × 23
23 = 23 × 1
Hence, the factors of 23 are 1 and 23
(i) 36
36 = 1 × 36
36 = 2 × 18
36 = 3 × 12
36 = 4 × 9
36 = 6 × 6
Thus the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
Q2. Write first five multiples of:
(a) 5
(b) 8
(c) 9
Solutions:
(a) The required multiples are:
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
Hence, the first five multiples of 5 are 5, 10, 15, 20 and 25
(b) The required multiples are:
8 × 1 = 8
8 × 2 = 16
8 × 3 = 24
8 × 4 = 32
8 × 5 = 40
Hence, the first five multiples of 8 are 8, 16, 24, 32 and 40
(c) The required multiples are:
9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45
Hence, the first five multiples of 9 are 9, 18, 27, 36 and 45
Q3. Match the items in column 1 with the items in column 2.
Column 1 Column 2
(i) 35 (a) Multiple of 8
(ii) 15 (b) Multiple of 7
(iii) 16 (c) Multiple of 70
(iv) 20 (d) Factor of 30
(v) 25 (e) Factor of 50
(f) Factor of 20
Solutions:
(i) 35 is a multiple of 7
Hence, option (b)
(ii) 15 is a factor of 30
Hence, option (d)
(iii) 16 is a multiple of 8
Hence, option (a)
(iv) 20 is a factor of 20
Hence, option (f)
(v) 25 is a factor of 50
Hence, option (e)
Q4. Find all the multiples of 9 upto 100.
Solutions:
9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45
9 × 6 = 54
9 × 7 = 63
9 × 8 = 72
9 × 9 = 81
9 × 10 = 90
9 × 11 = 99
∴ All the multiples of 9 up to 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 and 99
