Short answer: 360 = 2³ × 3² × 5, which gives (3+1)(2+1)(1+1) = 24 divisors and their sum is 1,170. 97 is prime, so its only divisors are 1 and itself.
Why factorisation is useful
It is the base of fraction simplification, LCM and GCD, and the reason 1/6 and 1/4 share a denominator of 12. In computing it sizes hash tables and underpins modular arithmetic, which is why the difficulty of factoring large numbers keeps RSA keys safe.
Worked example
2,310 = 2 × 3 × 5 × 7 × 11 — five distinct primes, so it has 2⁵ = 32 divisors. Finding that by hand means dividing by 2, 3, 5, 7 and 11 in turn, which is exactly what the calculator does, stopping at the square root.