Type a whole number and see its factor tree drawn branch by branch until every branch ends in a circled prime. Choose balanced, smallest-prime or random splits, get the answer in exponent form with the steps, and print a blank practice tree for students.
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How to use the Factor Tree Generator
Type a whole number such as 360, or tap an example.
Choose how to split: balanced pairs give the classic textbook tree, smallest prime first gives a ladder-shaped tree.
Press Draw factor tree to see the diagram, the exponent form and the steps.
Switch Show to a practice mode to hide the primes or every number except the top one.
Print the tree or download it as PNG or SVG for slides and worksheets.
Factor trees of common numbers
Number
One possible first split
Prime factorization
24
4 × 6
2³ × 3
36
6 × 6
2² × 3²
48
6 × 8
2⁴ × 3
60
6 × 10
2² × 3 × 5
72
8 × 9
2³ × 3²
84
7 × 12
2² × 3 × 7
90
9 × 10
2 × 3² × 5
100
10 × 10
2² × 5²
120
10 × 12
2³ × 3 × 5
360
18 × 20
2³ × 3² × 5
1,001
7 × 143
7 × 11 × 13
Tips for finding factor pairs quickly
Even numbers always split as 2 × half the number.
Ends in 0 or 5: 5 is a factor; ends in 0 means 10 = 2 × 5 is a factor.
Digit sum divisible by 3 (or 9): then 3 (or 9) is a factor. 378 → 3 + 7 + 8 = 18, so 378 = 9 × 42.
Start with a big, friendly pair like 10 × 36 instead of 2 × 180; the tree stays shorter and easier to check.
Check your answer by multiplying the circled primes back together; you should get the number at the top.
What factor trees are used for
Prime factorizations make other topics easier: the greatest common factor is the product of the primes two numbers share (lowest powers), the least common multiple uses every prime at its highest power, and a fraction is in lowest terms when the numerator and denominator share no prime. For example 36 = 2² × 3² and 60 = 2² × 3 × 5, so GCF = 2² × 3 = 12 and LCM = 2² × 3² × 5 = 180.
Frequently asked questions
What is a factor tree?
A factor tree is a diagram that breaks a number into a pair of factors, then breaks each factor again, until every branch ends in a prime number. The primes at the ends of the branches multiplied together give the prime factorization, for example 360 = 2³ × 3² × 5.
How do you make a factor tree?
Write the number at the top. Find any two factors that multiply to it (other than 1 and the number) and draw them as two branches. Repeat for each factor that is not prime. Circle each prime as you reach it. When every branch ends in a circle, write the circled primes in order.
Can a number have more than one factor tree?
Yes. 360 can start as 18 × 20, 10 × 36 or 2 × 180, and each start gives a different-looking tree. By the Fundamental Theorem of Arithmetic every tree ends with exactly the same primes, so the prime factorization is always the same. Use Random factor pair to see this.
What is exponent form?
Exponent form writes repeated prime factors with a power instead of repeating them: 2 × 2 × 2 × 3 × 3 × 5 becomes 2³ × 3² × 5. The primes are usually listed from smallest to largest.
What does the factor tree of a prime number look like?
A prime number has no factor pair other than 1 and itself, so its tree is just the number, circled. The generator tells you when a number is prime. The number 1 is neither prime nor composite and has no factor tree.
How do I make a factor tree worksheet?
Draw the tree, choose Show: Hide the primes or Blank tree, top number only, and press Print tree. The page includes a name line and instructions. Switch back to All numbers and print again to make the answer key.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.