All divisors of 60

Statement

List all positive divisors of $60$ and state how many there are.

Solution

Factor into primes: $60 = 2^2\cdot 3\cdot 5.$ The number of divisors is obtained by adding $1$ to each exponent and multiplying: $(2+1)(1+1)(1+1) = \boxed{12}.$ The divisors are $1,\;2,\;3,\;4,\;5,\;6,\;10,\;12,\;15,\;20,\;30,\;60.$