Find prime factors of 1000
Break any number into its prime factors with a complete factor tree.
1000
Divide 1000 by the smallest prime factors repeatedly:
Step 1: Is 1000 divisible by 2?
1000 is even (last digit is 0)
1000 ÷ 2 = 500
Step 2: Is 500 divisible by 2?
500 is even (last digit is 0)
500 ÷ 2 = 250
Step 3: Is 250 divisible by 2?
250 is even (last digit is 0)
250 ÷ 2 = 125
Step 4: Is 125 divisible by 5?
last digit is 5 (0 or 5)
125 ÷ 5 = 25
Step 5: Is 25 divisible by 5?
last digit is 5 (0 or 5)
25 ÷ 5 = 5
Step 6:
5 ÷ 5 = 1
Prime factorization (expanded):
1000 = 2 × 2 × 2 × 5 × 5 × 5
In exponential form:
1000 = 23 × 53
1000 = 23 × 53
How to find prime factors of 1000
To find the prime factorization of 1000, 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 1000?
The answer is 1000 = 2³ × 5³.
What method is used?
repeated division — divide by 2, then 3, then 5, and so on until the quotient is 1.