Question

Question 3 Using divisibility tests, determine which of following numbers are divisible by 6: (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

Class 6 - Math - Playing with Numbers Page 57

Answer 1

A number is divisible by another number if it leaves no remainder. Divisibility test helps us to check quickly if a number is divisible by another number or not.

Divisibility of numbers by 6

If a number is divisible by 2 & 3 , it is also divisible by 6..
                                 or
A number is divisible by 6 which has 0,2,4,6,8 at its one place & sum of its digits is divisible by 3
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Solution:

(a) 297144⇒ Divisible by 2 as its units place is an even number.

 ⇒Divisible by 3 as sum of its digits (= 27) is divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.

(b) 1258 ⇒ Divisible by 2 as its units place is an even number.

⇒Not divisible by 3 as sum of its digits (= 16) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(c) 4335⇒ Not divisible by 2 as its units place is not an even number.

⇒Divisible by 3 as sum of its digits (= 15) is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(d) 61233 ⇒Not divisible by 2 as its units place is not an even number.

⇒Divisible by 3 as sum of its digits (= 15) is divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(e) 901352 ⇒ Divisible by 2 as its units place is an even number.

⇒ Not divisible by 3 as sum of its digits (= 20) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(f) 438750 ⇒ Divisible by 2 as its units place is an even number.

⇒Divisible by 3 as sum of its digits (= 27) is not divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(g) 1790184 ⇒ Divisible by 2 as its units place is an even number.

⇒Divisible by 3 as sum of its digits (= 30) is not divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(h) 12583 ⇒ Not divisible by 2 as its units place is not an even number.

⇒ Not divisible by 3 as sum of its digits (= 19) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

(i) 639210 ⇒ Divisible by 2 as its units place is an even number.

⇒ Divisible by 3 as sum of its digits (= 21) is not divisible by 3.

Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

(j) 17852 ⇒ Divisible by 2 as its units place is an even number.

⇒ Not divisible by 3 as sum of its digits (= 23) is not divisible by 3.

Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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Hope this will help you....

Answer 2

ONLY A PART (a) 297144= Divisible by 2 as its units place is an even number.

 =Divisible by 3 as sum of its digits (= 27) is divisible by 3.