jmc

Question

The ''roundness'' of an integer greater than 1 is the sum of the exponents of the prime factorization of the number. For example, 20 = 2^2 5^1, so 20 has a roundness of 3. What is the roundness of 1,000,000?

Accepted Answer

1,000,000=10^6=(25)^6=2^65^6. The roundness of 1,000,000 is therefore 6+6=12.