Question

A number N when divided by 14 gives remainder 5. What is the remainder the same number is divided by 7?​

Answer 1

Let the number be X

Since dividing the number gives remainder as 5, X can be written as 14*Y + 5

where Y will be the quotient on dividing X by 14.

X = 14*Y + 5

X = 2*7*Y + 5

Lets divide both sides by 7 (since we want to know the remainder when X is divided by 7)

X/7 = (2*7*Y)/7 + 5/7

X/7 = 2*Y + 5/7

Since Y is a whole number (quotient), thus 2*Y will also be a whole number and what remains is 5/7.

Thus, the remainder is 5 when X is divided by 7.