Question

A positive integer when divided by 88 gives the remainder 61.what will be the remainder when the same number is divided by 11?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Remainder left is 6.

Step-by-step explanation:

Given: A Positive Integer number when divided by 88 gives remainder = 61

To find: Remainder when same number divided by 11.

Let n be that positive integer number.

According to Division algorithm,

n = q × 88 + 61

⇒ n - 61 = q × 88

So, ( n - 61 ) is divisible by 88.

We know that a number is divisible by all the factors of the divisor.

⇒ ( n - 61 ) is also divisible by 11

Hence,  ( ( n - 55 ) - 6 ) is divisible by 11.

Since 55 is divisible by 11.

⇒  (n-6) is divisible by 11.

 

It means that the number n gives the remainder 6 when is divided by 11.

Therefore, Remainder left is 6.