Question

Which of the following numbers is divisible by 6?
A. 1258
B. 61233
C. 901352
D. 1790184

Answer 1

Hint: In the given question, we are asked to find the options in which the numbers are divisible by 6. We know that, for a number to be divisible by 6, the number should be divisible by 2 and 3. A number is divisible by 2 if the number is even and a number is divisible by 3, if the sum of the digits of the number is divisible by 3. We will check the divisibility of each of the numbers in each of the cases. Hence, we will have the required option.

Complete step by step solution:
According to the given question, we are asked to find the number from the options which is divisible by 6.
We know that, to check a number if it is divisible by 6, we have to first check if the number is divisible by 2 and 3.
A number is divisible by 2 only when the number is an even number.
And a number is divisible by 3 only if the sum of the digits of the number is divisible by 3. So, we will check each of the options and see if it is divisible by 6 or not.
First we have, 1258
We can see that the number is even so it is divisible by 2, as the unit place of the number is 8 which is a multiple of 2.
The sum of the digits is, \[1+2+5+8=16\]. Since 16 is not divisible by 3,
Therefore, 1258 is not divisible by 6.
Next, we have, 61233
We can clearly see that the unit place of the number is 3 which is not divisible by 2.
Therefore, the number 61233 is not divisible by 6.
Next, we have, 901352
The number has the unit place as 2 which is divisible by 2, so the number is divisible by 2.
The sum of the digits is, \[9+0+1+3+5+2=20\]. Since, 20 is not divisible by 3,
Therefore, the number 901352 is not divisible by 6.
Next number we have is, 1790184
As the number has an even number at the unit’s place, so the number is divisible by 2.
The sum of the digits is, \[1+7+9+0+1+8+4=30\], since 30 is divisible by 3,
Therefore, the number 1790184 is divisible by 6.

Note: The notion between a number being odd or even should be clear. The number having multiples of 2 in the unit’s place is even and the rest of the numbers are odd. Also, while checking the divisibility by 3, the sum of the digits should be done clearly and correctly.