Prime numbers
Each student of a grade 7 class at École Sainte-Anne is given a list of the first 100 prime numbers and asked to pick 4 distinct numbers from the list.
Alexane finds the product and the sum of her 4 numbers and she notices that the sum divides the product.
What is the smallest of Alexane's 4 numbers?
The answer is 2.
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1 solution
All prime numbers with the exception of 2 are odd.
The product of four odd numbers is odd and the sum of four odd numbers is even.
An even sum *does not * divide exactly in an odd product.
The only even prime is 2.
Alexane's must have chosen 2 so that her product is even and her sum is odd (even+odd+odd+odd= odd).
An odd sum may divide exactly an even product.
eg 2, 3, 11 and 17
sum=33
product=1122
1122/33=34