Find the smallest number which should be added to 1234 to get a number divisible by 45.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 26.
Let the required number = 1234 + x ≡ 0 (mod45)
x ≡ −1234 (mod45) ⇒ x ≡ (45 − (1234 mod 45))
1234 ÷ 45 = 27 remainder 19 ⇒ 1234 mod 45 = 19
So:
x = 45 − 19 = 26