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Prime Numbers and Prime Factorization
A prime number has exactly two positive factors, 1 and itself; prime factorization writes a composite number as a product of primes.
How it works
Divide by the smallest possible prime and keep dividing each composite result until only primes remain. The fundamental theorem of arithmetic says every integer greater than 1 has one prime factorization, apart from the order of the factors.
Worked example
Find the prime factorization of 84.
- 84 = 2 × 42.
- 42 = 2 × 21.
- 21 = 3 × 7.
- All remaining factors are prime.
84 = 2² × 3 × 7.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Treating 1 as a prime number.
- Stopping with a composite factor such as 6.
- Listing prime factors without showing repeated factors.
Challenge
Find the smallest number with prime factorization 2³ × 3² × 5.
Questions learners ask
Is 1 a prime number?
No. A prime must have exactly two positive factors, while 1 has only one.
Why is prime factorization unique?
Every integer greater than 1 breaks into the same prime factors, except for their order.