Question

Which number(s) must be subtracted from $4070$ to make it divisible by $8?$

• A. $30$
• B. $45$
• C. $806$
• D. $1605$

Answer 1

Answer: (A), (C)

$806$

When we divide last three digits of $4070$ by 8, we get 6 as remainder.

That means, if we subtract 6 from the number i.e. $4070-6=4064$, then the resulted number i.e. $4064$ would be divisible by 8.

Now, if we subtract 8 or mutiples of 8 from $4064$, resulted difference would be divisible by 8.

Hence if we subtract $(6+8n,\text{where}n\text{is an integer})$ from 4070, resulted difference would be definately divisible by 8.

Option(a):
$\because 30=6+8\times 3$
Hence, $(4070-30)$ is divisible by 8.

Option(b):
$\because 45\ne 6+8\times 5$
Hence, $(4070-45)$ is not divisible by 8.

Option(c):
$\because 806=6+8\times 100$
​​​​​​​Hence, $(4070-806)$ is divisible by 8.

Option(d):
$\because 1605\ne 6+8\times 200$
​​​​​​​Hence, $4070-1605$ is not divisible by 8.