Question

find the greatest number that will divide 80,118 and 60 leaving remainders 8,10 and 12 respectively
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Answer 1

Answer:

The greatest number that will divide 80,118 and 60 leaving remainder 8,10 and 0 is 12.

Answer 2

Answer:

80 remainer 8 is a number that evenly divides 72.

118 remainder 10 is a number that evenly divides 108.

60 remainder 12 is a number that evenly divides 48.

However, since the remainders are 8, 10, and 12 we know that x must be greater than 12.

From here the solution is GCD of 72, 108, and 48.

Looking at 72′s factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

We can start at a small range, since 12 and smaller can't be our number due to the largest remainder being 12. 36 and 72 are too large to be factors of 48 so those are also eliminated. That leaves us with 18 and 24. 18 is not a factor of 48 so 24 must be the number we are looking for. But just to be safe, 108/24=4.5. Uh oh. Either I did my math wrong or there is no solution to this problem.

If we decided to ignore the fact that 12 evenly divides 60 then the solution would be 12.