Multiple choice

The greatest number that will divide 729 and 901 leaving remainders 9 and 5, respectively, is

  1. 15

  2. 16

  3. 19

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number must divide (729 - 9) = 720 and (901 - 5) = 896. The greatest common divisor of 720 and 896 is 16.

AI explanation

To find the greatest number that leaves specific remainders, we subtract the remainders from the respective numbers and find their Highest Common Factor (HCF). The resulting numbers are 729 minus 9, which equals 720, and 901 minus 5, which equals 896. Applying the Euclidean algorithm to find the HCF of 720 and 896, we find that 896 divided by 720 leaves a remainder of 176, and 720 divided by 176 leaves a remainder of 16. The greatest number is 16.

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