Multiple choice

The greatest four-digit number when divided by 4, 7 and 13 leaves a remainder of 3 in each case. Find the number.

  1. 8739

  2. 9831

  3. 9834

  4. 9893
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The LCM of 4, 7, and 13 is 364. The greatest four-digit number is 9999. Dividing 9999 by 364 gives 27 with a remainder of 183. 9999 - 183 = 9816. Adding the remainder 3 gives 9819. Checking options, 9831 is not divisible by 364 with remainder 3. 9831 / 4 = 2457 R 3, 9831 / 7 = 1404 R 3, 9831 / 13 = 756 R 3. The calculation 9831 is correct.

AI explanation

Find the least common multiple (LCM) of 4, 7 and 13 to get 364. The greatest four-digit number is 9999; dividing 9999 by 364 gives a quotient of 27 and a remainder of 171. Multiply the quotient 27 by 364 to get the greatest four-digit multiple of 364, which is 9828; adding the required remainder of 3 gives 9831.

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