Question

Using the method of remainder of the place value, find which of these numbers is divisible by 6.

• A. 963451
• B. 750216
• C. 451931
• D. 573842

Answer 1

The correct option is B 750216

In this method we take remainders by dividing the place values, with the given number which is 6 in our case.

If we divide the place values of a number by 6, we get the remainders as

Place Value	${10}^5$	${10}^4$	${10}^3$	${10}^2$	${10}^1$	${10}^0$
Remainders divide by 7	$4$	$4$	$4$	$4$	$4$	$1$

Now to check whether 963451 is divisible by 6 or not

Digits	$9$	$6$	$3$	$4$	$5$	$1$
Place Value	${10}^5$	${10}^4$	${10}^3$	${10}^2$	${10}^1$	${10}^0$
Remainders divide by 7	$9\times 4$	$6\times 4$	$3\times 4$	$4\times 4$	$5\times 4$	$2\times 1$

Sum of product of face values and remainders of the place values is 110(not divisible by 6)
Hence, 963451 is not divisible by 6.

To check whether 750216 is divisible by 6 or not

Digits	$7$	$5$	$0$	$2$	$1$	$6$
Place Value	${10}^5$	${10}^4$	${10}^3$	${10}^2$	${10}^1$	${10}^0$
Remainders divide by 7	$7\times 4$	$5\times 4$	$0\times 4$	$2\times 4$	$1\times 4$	$6\times 1$

Sum of product of face values and remainders of the place values is 66(divisible by 6)
Thus, 750216 is divisible by 6.

To check whether 451931 is divisible by 6 or not

Digits	$4$	$5$	$1$	$9$	$3$	$1$
Place Value	${10}^5$	${10}^4$	${10}^3$	${10}^2$	${10}^1$	${10}^0$
Remainders divide by 7	$4\times 4$	$5\times 4$	$1\times 4$	$9\times 4$	$3\times 4$	$1\times 1$

Sum of product of face values and remainders of the place values is 89(not divisible by 6)
So, 451931 is not divisible by 6.

To check whether 573842 is divisible by 6 or not

Digits	$5$	$7$	$3$	$8$	$4$	$2$
Place Value	${10}^5$	${10}^4$	${10}^3$	${10}^2$	${10}^1$	${10}^0$
Remainders divide by 7	$5\times 4$	$7\times 4$	$3\times 4$	$8\times 4$	$4\times 4$	$2\times 1$

Sum of product of face values and remainders of the place values is 110(not divisible by 6)
Therefore, 573842 is not divisible by 6.