Level: 6 - 9, middle

Asking: Student

Question:

When 391 758 and 394 915 are divided by a certain three digit numbers, the three digit remainder is the same in each case. Find the divisor.

Hi Kim

Since 391 758 and 394 915 have the same remainder when divided by a certain three digit number, the difference between 391 758 and 394 915 will have a remainder of zero when divided by this number. 394 915 - 391 758 = 3 157. But 3 157 = 7*11*41 so 3 157 is divisible by 7, 11, 41, 7*11=77, 7*41=287, 7*41=451 and 7*11*41=3 157. Hence the three didgit divisors are 287 and 451 and thus you need to determine which gives a three digit remainder when divided into 391 758 and 394 915.

Cheers

Penny

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