Free Factor Tree Generator

Write the composite number at the top, choose any factor pair greater than 1, and draw those two factors as branches. Repeat the process for every composite factor. Stop only when every final leaf is prime, then multiply the prime leaves to check that they equal the original number.

Yes. A composite number may have several factor pairs, so different first splits can create different tree shapes. For 60, you could begin with 6 × 10, 4 × 15, or 3 × 20. Every valid completed tree still ends with the same unique prime factorization: 2² × 3 × 5.

A prime number has no factor pair other than 1 and itself, so it cannot branch into smaller whole-number factors. The generator shows it as one labeled prime leaf instead of returning an error. For example, the complete prime factorization of 97 is simply 97.

The number 1 is neither prime nor composite. A prime number must have exactly two positive factors: 1 and itself. Including 1 as a prime factor would also make every factorization endlessly repeatable, because any product could contain an unlimited number of extra factors of 1.

This classroom generator accepts positive whole numbers greater than 1. Standard factor trees describe integer prime factorization, so decimals are not valid inputs. A negative integer can be written with an additional factor of −1, but the visible tree normally uses its positive part.

Turn on Compare two numbers and enter the second integer. The generator factors both numbers and aligns every prime in an exponent table. GCF multiplies shared primes using the smaller exponent; LCM uses every prime with its larger exponent. For 60 and 84, the tool shows GCF = 12 and LCM = 420.

A factor tree splits a number into two factors at each branch, so you can see how composite parts connect. The ladder method repeatedly divides the number by primes in a vertical list. The layouts differ, but both methods produce the same prime factorization when completed correctly.

Yes. Switch the preview to Worksheet mode to hide the prime leaf values while keeping the branch structure. Print that version for a paper exercise, then return to Answer mode to review the completed factor tree. You can also download SVG or PNG files for lesson materials.