Using Exponents

A factor tree often ends with the same prime many times. 1,024 ends with ten 2s.

Write a repeated prime as a power: $2\cdot 2\cdot 2$ is ${2}^{3}$. The small number is the exponent. It counts how many times the prime repeats. So 1,024 is ${2}^{10}$, and 360 is ${2}^{3}\cdot {3}^{2}\cdot 5$.

For a big number, split off small primes first. A last digit of 0 means 2 and 5 are factors. A digit sum of 9 means 3 and 3 are factors.