NCERT Class 6 Mathematics Third Chapter Playing with Numbers Exercise 3.3 Solutions

NCERT Class 6 Mathematics Third Chapter Playing with Numbers Exercise 3.3 Solutions

EXERCISE 3.3

(1) Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):

(2) Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:

(a) 572 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

(b) 726352 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

Divisible by 8; because the last three digits is divisible by 8

(c) 5500 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

(d) 6000 = Divisible by 4; Divisible by 8, because the last three digits is divisible by 8

(f) 14560 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

Divisible by 8; because the last three digits is divisible by 8

(g) 21084 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

(h) 31795072 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

Divisible by 8, because the last three digits is divisible by 8

(i) 1700 = Divisible by 4; because its last two digits (i.e. ones and tens) is divisible by 4.

(3) Using divisibility tests, determine which of following numbers are divisible by 6:

Ans: (a) 297144, (f) 438750, (g) 1790184, (i) 639210

(4) Using divisibility tests, determine which of the following numbers are divisible by 11:

(a) 5445

Solution: (5 + 4) – (5 + 4)

= 9 – 9 = 0

So, 5445 is divisible by 11.

(b) 10824

Solution: (1 + 8 + 4) – 2

= 13 – 2 = 11

So, 10824 is divisible by 11.

(c) 7138965

Solution: (7 + 3 + 9 + 5) – (1 + 8 + 6)

= 24 – 15 = 9

So, 7138965 is not divisible by 11.

(d) 70169308

Solution: (7 + 1 + 9) – (6 + 3 + 8)

= 17 – 17 = 0

So, 70169308 is divisible by 11.

(e) 10000001

Solution: 1 – 1 = 0

So, 10000001 is divisible by 11.

(f) 901153

Solution: (9 + 1 + 5) – (1 + 3)

= 15 – 4 = 11

So, 901153 is divisible by 11.

(5) Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3:

(a)  26724

Solution: (6 + 7 + 2 + 4) = 19 + 2 = 21, which is divisible by 3. So, the required number is 2.

(b) 476582

(6) Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:

(a) 928389

Solution: (9 + 8 + 8) – (2 + 3 + 9)

= 25 – 14 = 11

So, the required number is 8.

(b) 869484

Solution: (8 + 9 + 8) – (6 + 4 + 4)

= 25 – 14 = 11

So, the required number is 6.