Question

A number divided by 372 leaves a remainder of 65.what is the remainder when the same number is divided by 31?​

Answer 1

Let the number be x

By Euclid's division lemma

x=143q+31 where q is quotient

=143q+26+5

x=13 (11q+2)+5

x=13p+5 where p is quotient of form 11q+2

.’. 5 is the remainder

Answer 2

SOLUTION

GIVEN

A number divided by 372 leaves a remainder of 65

TO DETERMINE

The remainder when the same number is divided by 31

EVALUATION

Here it is given that a number divided by 372 leaves a remainder of 65

Then Divisor = 372 , remainder = 65

Let quotient = m

The the number

= Divisor × Quotient + Reminder

= 372m + 65

Now we divide the number by 31

372 is completely divisible by 31

∴ 372m is completely divisible by 31

Again if we divide 65 by 31 , the Remainder = 3

Hence the required Remainder = 3

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