Find prime factors of 360
Break any number into its prime factors with a complete factor tree.
360
Divide 360 by the smallest prime factors repeatedly:
Step 1: Is 360 divisible by 2?
360 is even (last digit is 0)
360 ÷ 2 = 180
Step 2: Is 180 divisible by 2?
180 is even (last digit is 0)
180 ÷ 2 = 90
Step 3: Is 90 divisible by 2?
90 is even (last digit is 0)
90 ÷ 2 = 45
Step 4: Is 45 divisible by 3?
digit sum = 9 (divisible by 3)
45 ÷ 3 = 15
Step 5: Is 15 divisible by 3?
digit sum = 6 (divisible by 3)
15 ÷ 3 = 5
Step 6:
5 ÷ 5 = 1
Prime factorization (expanded):
360 = 2 × 2 × 2 × 3 × 3 × 5
In exponential form:
360 = 23 × 32 × 5
360 = 23 × 32 × 5
How to find prime factors of 360
To find the prime factorization of 360, 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 360?
The answer is 360 = 2³ × 3² × 5.
What method is used?
repeated division — divide by 2, then 3, then 5, and so on until the quotient is 1.