How do you calculate the number of factors in the number 2310?

Answer 1

The prime factorization of 2310 is 2 x 3 x 5 x 7 x 11. All of those numbers have an implied exponent of 1. If you add 1 to each exponent and multiply them, the total will equal the number of factors.

2 x 2 x 2 x 2 x 2

2310 has 32 factors.

Answer 2

Find the prime factorisation of 2310 and write it in index form : (p1^n1)*(p2^n2)* ... *(pk^nk)where p1, p2, ... pk are distinct prime numbers and the n1, n2, ... nk are integers.

Add one to each power and multiply these numbers together. That is (n1+1)*(n2+1)*...*(nk+1)

In this particular case,

2310 = 2*3*5*7*11 = (2^1)*(3^1)*(5*1)*(7^1)*(11^1)

So, n1=n2=n3=n4=n5 = 1 and so the number of factors is 2*2*2*2*2 = 32.

The 32 factors include 1 and 2310.