Selina Concise Class 6 Math Chapter 9 Playing With Numbers Exercise 9A Solution
EXERCISE 9A
(1) Fill in the blanks:
(i) On dividing 9 by 7, quotient = 1 and remainder = 2.
(ii) On dividing 18 by 6, quotient = 3 and remainder = 0.
(iii) Factor of a number is exact divisor of the number.
(iv) Every number is a factor of itself.
(v) Every number is a multiple of one and itself.
(vi) One is factor of every number.
(vii) For every number, its factors are finite and its multiples are infinite.
(viii) x is a factor of y, then y is a multiple of x.
(2) Write all factors of:
(i) 16 = 1, 2, 4, 8, 16
(ii) 21 = 1, 3, 7, 21
(iii) 39 = 1, 3, 13, 39
(iv) 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
(v) 64 = 1, 2, 4, 8, 16, 32, 64
(vi) 98 = 1, 2, 7, 14, 49, 98
(3) Write the first six multiples of:
(i) 4 = 4 , 8, 12, 16, 20, 24
(ii) 9 = 9, 18, 27, 36, 45, 54
(iii) 11 = 11, 22, 33, 44, 55, 66
(iv) 15 = 15, 30, 45, 60, 75, 90
(v) 18 = 18, 36, 54, 72, 90, 108
(vi) 16 = 16, 32, 48, 64, 80, 96
(4) Since, 36 = 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Clearly numbers are 4 and 9.
(5) Since, 48 = 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8
Clearly, numbers are 4 and 12.
(6) Let the two numbers be x and (x – 3).
We have, x (x – 3) = 54
⇒ x2 – 3x – 54 = 0
⇒ x2 – (9 – 6)x – 54 = 0
⇒ x2 – 9x + 6x – 54 = 0
⇒ x (x – 9) + 6(x – 9) = 0
⇒ (x – 9) (x + 6) = 0
Hence, x + 6 = 0 ⇒ x = – 6 and x – 9 = 0⇒ x = 9.
(7) 7000 = 7000 + 7 = 7 × (1000 + 1) = 7 × 1001
Clearly, 7007 is divisible by 7.
(8) 2300023 = 2300000 + 23 = 23 (100000 + 1) = 23 × 100001
Clearly, 2300023 is divisible by 23.
(9) (i) 11011 = 11000 + 11 = 11 × (1000 + 1) = 11 × 1001
Clearly, 11011 is divisible by 11.
(ii) 110011 = 110000 + 11 = 11 × (10000 + 1) = 11 × 10001
Clearly, 110011 is divisible by 11.
(iii) 11000011 = 11000000 + 11 = 11 × (1000000 + 1) = 11 × 1000001
Clearly, 11000011 is divisible by 11.
(10) (i) 1608 = 1600 + 8 = 8 (200 + 1) = 8 × 201
Clearly, 1608 is divisible by 8.
(ii) 56008 = 56000 + 8 = 8 (7000 + 1) = 8 × 7001
Clearly, 56008 is divisible by 8.
(iii) 24008 = 24000 + 8 = 8 (3000 + 1) = 8 × 3001
Clearly, 24008 is divisible by 8.