2.5

[TakaiKinoko]

I'll suggest a corner case to your algorithm: 40, which can't be reduced to the product of 2^a and 3^b.

[bfjei2825401]

The pair number is regarded as the exponents of 2 and 3 respectively, so the product 2^a and 3^b can only be divided by 2 and 3 (no other prime number factors).