Question

Test the divisibility of the following numbers by 6:

(i) 7020
(ii) 56423
(iii) 732510

Answer 1

Rule: A number is divisible by 6 if it is divisible by 2 as well as 3.

(i) Here, the unit's digit = 0
Thus, the given number is divisible by 2.
Also, the sum of the digits = 7 + 0 + 2 + 0 = 9 which is divisible by 3. So, the given number is divisible by 3.
Hence, 7,020 is divisible by 6.

(ii) Here, the unit's digit = 3
Thus, the given number is not divisible by 2.
Also, the sum of the digits = 5 + 6 + 4 + 2 + 3 = 20 which is not divisible by 3. So, the given number is not divisible by 3.
Since 3,56,423 is neither divisible by 2 nor by 3, it is not divisible by 6.

(iii) Here, the unit's digit = 0
Thus, the given number is divisible by 2.
Also, the sum of the digits = 7 + 3 + 2 + 5 + 1 + 0 = 18 which is divisible by 3. So, the given number is divisible by 3.
Hence, 7,32,510 is divisible by 6.