On dividing a number by 357 we get w as remainder. On dividing the same number 17 what will be the remainder?

Answer 1

If x ≡ w mod 357 then:

x = 357k + w for some integer k.

Now 357 = 21×17, and w = 17n + c for some integers n ≥ 0 and 0 ≤ c < 17

→ w ≡ c mod 17

This gives:

x = 21×17×k + 17n + c

→ x = 17(21k + n) + c

→ x = 17m + c where m = 21k + n (is an integer)

→ x ≡ c mod 17

→ the remainder when the number is divided by 17 is the same as the remainder when the original remainder w is divided by 17.