Question

Taking remainders of place values, find which of the following number is divisible by 7.

• A. 562499
• B. 123456
• C. 234567
• D. 114789

Answer 1

The correct option is A 562499

If we divide the place values of a number by 7, we get the remainders as
100000 ÷ 7 = (Remainder 5)
(This can be taken as 5 - 7 = −2)
10000 ÷ 7 = (Remainder 4)
(This can be taken as 4 - 7 = −3)
1000 ÷ 7 (Remainder 6)
(This can be taken as 6 - 7 = −1)
100 ÷ 7 (Remainder 2)
10 ÷ 7 (Remainder 3)
1 ÷ 7 (Remainder 1)

To check the divisibility by 7

Digits	Place value	Product of face value and remainder of place value
5	500000	5 x (-2)
6	60000	6 x (-3)
2	2000	2 x (-1)
4	400	4 x 2
9	90	9 x 3
9	9	9 x 1

Product of face value and remainder of place value
= - 10 - 18 - 2 + 8 + 27 + 9
= 14
which is divisible by 14.
Similarly, if we check for the rest of the numbers. It is not divisible by 7.
$\therefore$ 562499 is divisible by 7.