Product 100
The product of four different positive integers is 100. What is the sum of these four integers?
Age
11 to 14
Challenge level
Problem
The product of four different positive integers is 100.
What is the sum of these four integers?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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