Find prime factors of 420
Break any number into its prime factors with a complete factor tree.
420
Divide 420 by the smallest prime factors repeatedly:
Step 1: Is 420 divisible by 2?
420 is even (last digit is 0)
420 ÷ 2 = 210
Step 2: Is 210 divisible by 2?
210 is even (last digit is 0)
210 ÷ 2 = 105
Step 3: Is 105 divisible by 3?
digit sum = 6 (divisible by 3)
105 ÷ 3 = 35
Step 4: Is 35 divisible by 5?
last digit is 5 (0 or 5)
35 ÷ 5 = 7
Step 5:
7 ÷ 7 = 1
Prime factorization (expanded):
420 = 2 × 2 × 3 × 5 × 7
In exponential form:
420 = 22 × 3 × 5 × 7
420 = 22 × 3 × 5 × 7
How to find prime factors of 420
To find the prime factorization of 420, start dividing by the smallest prime factor (2), then try 3, 5, 7, and so on until the quotient is 1. Each prime factor and its power make up the factorization.
This is a prime factorization — every integer greater than 1 has a unique prime factorization. We find it by dividing by the smallest primes.
Frequently asked questions
What is the answer to 420?
The answer is 420 = 2² × 3 × 5 × 7.
What method is used?
repeated division — divide by 2, then 3, then 5, and so on until the quotient is 1.