Question

What is the sum of the seven smallest composite numbers which cannot be determined to be composite simply by using the divisibility rules for 2,3,4,5,6,8,9 or 10?

Answer 1

My answer is 247.

Explanation:

I used guess and check, but if you can find a better way, please let me know.

32+33+34+35+36+38+39=247=13x19.

63 is not possible because it is divisible by 3 and 9.

Answer 2

63

Explanation:

A composite number is a whole number. It can be defined as a number that is divisible by 1, itself and other factors. This means a composite number has two or more factors. A prime number cannot be a composite number.

The seven smallest composite numbers are:

4, 6, 8, 9, 10, 14, 16,

Their total sum = 4 + 6 + 8 + 9 + 10 + 14 + 16 = 63

Therefore, the sum of the seven smallest composite numbers which cannot be determined to be composite simply by using the divisibility rules (for 2,3,4,5,6,8,9 or 10) is 63.