Question

I am the greatest common factor of three numbers. Their sum is 36. The largest number is twice the smallest and the middle number is the mean of the other two. What are the three numbers? What number am I?

Answer 1

let the 3 numbers be a , b, and c, in order of size, c is the largest

a+b+c = 36

c = 2a

b = (a+c)/2
= (a+2a)/2 = 3a/3

back into the first
a+b+c = 36
a + 3a/2 + 2a = 36
times 2
2a + 3a + 4a = 72
9a = 72
a = 8, then c = 16, and b = 12

Our 3 numbers are 8, 12, and 16
(all informations checks)

the greatest common factor of those is 4

Answer 2

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