Product 100
The product of four different positive integers is 100. What is the sum of these four integers?
The product of four different positive integers is 100.
What is the sum of these four integers?
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Answer: 18
100 = 50$\times$2$\times$1$\times$1 not all different
= 10$\times$5$\times$2$\times$1 good! Sum = 18
Is there another way?
Factors of 100 not used: 4, 20, 25
100 = 4$\times$25$\times$1$\times$1 not all different
= 4$\times$5$\times$5$\times$1 not all different. Cannot use 4
= 25$\times$2$\times$2$\times$1 not all different. Cannot use 25
100 = 20$\times$5$\times$1$\times$1 not all different. Cannot use 20