Start by dividing out a 2: 7020 = 2 x 3510
Since the answer is even, divide out another 2: 7020 = 2 x 2 x 1755
Since the sum of the digits of 1755 is 1 + 7 + 5 + 5 = 18 is divisible by 3, so is 1755:
7020 = 2 x 2 x 3 x 585
Since the sum of the digits of 585 is 5 + 8 + 5 = 18 is divisible by 3, so is 585:
7020 = 2 x 2 x 3 x 3 x 195
Since the sum of the digits of 195 is 1 + 9 + 5 = 15 is divisible by 3, so is 195:
7020 = 2 x 2 x 3 x 3 x 65
65 is not divisiible by 3, but it is divisible by 5:
7020 = 2 x 2 x 3 x 3 x 3 x 5 x 13