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When the numbers 312, 708, 697,and 279 are each divided by the same whole number, the remainder is the same. If the whole number is greater than one, what is this whole number?

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caylus
Hello,

Let's a=279-i with i=0 to 16
Let's b=312-i with i=0 to 16
Let's c=697-i with i=0 to 16
Let's d=708-i with i=0 to 16




I don't know how to solve this but
If n is the commun divider, it must be <√279=16.70...
Remainder must also be < n

We have to find the maximun of (a-i)∧(b-i)∧(c-i)∧(d-i) =11 (if i=4 or i=15 )

279=11*25+4
312=11*28+4
697=11*63+4
708=11*64+4
When i=15 ,n=11  but i must be<11
so only one solution n=11 and remainder=4


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