213.7143
29
59
58
57
213.7143
213.7143
213.7143
2519
29
59
58
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.
57
179 works until divided by 7 the remainder is 6. 2519 works till 10....
209
8976 + 638 - 234 = 9380