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

To find the remainder when a number N is divided by 7, we can use the concept of modular arithmetic.

Given that N divided by 14 gives a remainder of 5, we can express this as N ≡ 5 (mod 14), where "≡" denotes congruence.

To find the remainder when N is divided by 7, we need to find an equivalent congruence modulo 7.

Since 14 is divisible by 7, we can divide both sides of the congruence N ≡ 5 (mod 14) by 7 to obtain N/7 ≡ 5/7 (mod 14/7).

Simplifying, we have N/7 ≡ 5/7 (mod 2).

Now, we can express the remainder when N is divided by 7 as N ≡ 5/7 ≡ 1 (mod 2).

Therefore, the remainder when the same number N is divided by 7 is 1.