Step-by-step explanation:
we start with the first prime factor (2) and divide the number and then the result again (and again and again) until we cannot divide without remainder anymore.
then we go to next larger prime factor (3) and try the same. if we cannot divide without remainder, we go to the next larger prime factor (5) and repeat. and repeat. until we are down to dividing 1. then we are finished.
so,
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 2 no
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
1 finished
the prime factors of 120 are therefore
2, 3, 5
and the prime factor break down is
2×2×2×3×5 = 2³×3¹×5¹ = 120
