Question

What is the remainder when $(32540\times 42400\times 3233)+222$ is divided by 13?

• A. 0
• B. 1
• C. -1
• D. 11

Answer 1

The correct option is C -1

$32540$ using the divisibility test for 13 (triplets at odd - triplets at even places) can be written as:

$540-32=508.508$ when divided by 13 can be represented as $13k+1$ (i.e. when the number is divided by 13, the remainder is 1).

Similarly,

$42400=400-42=358=13l+7$

$3233=233-3=230=13m+9$

$(13k+1)(13l+7)(13m+9)$ will give the non-divisible part as $(9\times 7\times 1)=63$

Therefore $63+222=$ Remainder of 285 when divided by $13=-1$ or $12$.