Start With a Number
The tool gives you a composite whole number to factor completely.
Free Interactive Math Tool
Prime Factorization Practice
Build a factor tree using any valid factor pairs, continue splitting composite numbers until every branch ends in a prime number, and write the final prime factorization using exponents.
Learn Prime Factorization First
Learn how to identify prime and composite numbers, build factor trees using any valid factor pairs, and write prime factorizations using exponent notation before practicing with the interactive tool.
Read the Prime Factorization GuideHow It Works
Build a Factor Tree Step by Step
Choose any valid factor pair for each composite number. Continue building branches until every number at the bottom of the tree is prime.
Choose a Factor Pair
Enter any two whole-number factors whose product equals the number in the current branch.
Split Composite Factors
Keep factoring every composite result. Prime numbers become completed leaves automatically.
Write the Prime Factorization
Collect the prime leaves and combine repeated factors using exponent notation.
Interactive Practice
Prime Factorization
Correct
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Problems
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Streak
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Build a factor tree for
60
Split each composite number using any valid factor pair. The order of the factors does not matter.
1
Build Tree
2
List Primes
3
Final Answer
Step 1
Build the factor tree.
Select any composite leaf, enter two factors, and continue until every leaf is prime.
Factor this number
60
Factor tree complete.
Every leaf is now prime.
Step 2
List the prime factors.
Enter every prime leaf from the completed tree. Repeated prime factors must be entered more than once.
You may separate the factors with multiplication signs, commas, spaces, or the letter x.
Step 3
Write the prime factorization with exponents.
Combine repeated prime factors using exponent notation. Factors may be written in any order.
Use the caret symbol for exponents, such as 2^3. You may separate factors with ×, x, an asterisk, or spaces.
Great job!
You completed the factor tree and wrote the prime factorization correctly.
Remember
Prime Factorization Rules
Different factor trees can look different and still lead to the same prime factorization.
Any Valid Factor Pair Works
You may split a composite number using any pair of whole-number factors greater than one.
60 = 6 × 10
Keep Factoring Composite Numbers
A branch is not finished until its number is prime. Composite leaves must be split again.
10 = 2 × 5
Prime Leaves Are Finished
Prime numbers have exactly two positive factors: 1 and the number itself.
2, 3, 5, 7, 11
Combine Repeated Factors
Repeated prime factors can be written more compactly using exponents.
2 × 2 × 3 = 2² × 3
Why It Matters
Prime Factorization Builds Other Math Skills
Prime factorization helps students understand factors, divisibility, greatest common factors, least common multiples, fractions, and later algebra topics.
Greatest Common Factor
Compare prime factorizations and multiply the prime factors the numbers share.
Least Common Multiple
Use every required prime factor to build the smallest common multiple.
Simplifying Fractions
Identify common prime factors in the numerator and denominator, then divide them out.
Keep Practicing
Build Stronger Number-Sense Skills
Practice factor trees until you can recognize primes, composite numbers, factor pairs, and repeated prime factors with confidence.
Practice Another Factor Tree