Question

A number when divided by 703 gives a remainder of 75. what will be the remainder when we divide the same number by 37?

a) 1
b) 2
c) 5
d) 7

Answer 1

When a number that gives a remainder of 75 when divided by 703 is divided by 37, the remainder will be 1. Therefore, the remainder when the original number is divided by 37 is 2 (option b).

Step-by-step explanation:

The question asks what the remainder would be when a number that leaves a remainder of 75 when divided by 703 is divided by 37 instead.

This is a number theory problem involving remainders and division. Let's call the original number n. We can express n as n = 703k + 75, where k is the quotient when n is divided by 703. When we divide 75 by 37, we get a quotient of 2 and a remainder of 1.

Hence, if the original number n is divided by 37, the remainder will be 1, because 703 is divisible by 37 and thus leaves no remainder.

When a number is divided by 703, it leaves a remainder of 75. To find the remainder when the same number is divided by 37, we need to find a pattern between the remainders of dividing by 703 and dividing by 37.

We can do this by subtracting 703 from multiples of 37 until we find a number that gives a remainder of 75 when divided by 703. The closest multiple is 2, so when we divide 74 (which is 2 times 37) by 703, the remainder is 75. Therefore, the remainder when the original number is divided by 37 is 2 (option b).