Multiple choice

The numbers 11284 and 7655, when divided by a certain number of three digits, leave the same remainder. Find that number of three digits.

  1. 161

  2. 171

  3. 181

  4. 191

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If two numbers leave the same remainder when divided by N, then N must divide their difference exactly. Calculate 11284 - 7655 = 3629. Find the 3-digit factors of 3629 by prime factorization. 3629 = 19 × 191. The 3-digit divisors are 191 only (since 19 is 2-digit). Check: 11284 ÷ 191 = 59 remainder 15, and 7655 ÷ 191 = 40 remainder 15. Both leave remainder 15, confirming 191 is the answer.