Factor Tree & GCF / LCM Calculator

Enter one number to see its factor tree and prime factorization, or enter two numbers to find their Greatest Common Factor and Least Common Multiple. A Venn diagram shows which prime factors are shared and which are unique.

First number

Second number (optional)

Enter one number for its factor tree, or two numbers for GCF and LCM.

Try an example

Factor Trees

Factor tree of 12

Factor tree of 18

Prime Factor Venn Diagram

Prime Factorization

12 = 2^{2} \times 3

18 = 2 \times 3^{2}

GCF

6

Greatest Common Factor

LCM

36

Least Common Multiple

Check:

6 \times 36 = 216

and

12 \times 18 = 216

All Factors

12: 1, 2, 3, 4, 6, 12(6 factors)

18: 1, 2, 3, 6, 9, 18(6 factors)

Reference Guide

Prime Factorization

Every whole number greater than 1 can be written as a product of prime numbers. This is called its prime factorization.

60 = 2^2 \times 3 \times 5

A factor tree breaks a number down step by step. Split the number into any two factors, then keep splitting until every branch ends at a prime number.

Greatest Common Factor (GCF)

The GCF of two numbers is the largest number that divides both of them evenly. To find it using prime factorizations, multiply together the prime factors they have in common, using the smaller exponent for each.

12 = 2^2 \times 3

18 = 2 \times 3^2

\text{GCF} = 2 \times 3 = 6

Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that both divide into evenly. To find it, multiply all prime factors from both numbers, using the larger exponent for each.

12 = 2^2 \times 3

18 = 2 \times 3^2

\text{LCM} = 2^2 \times 3^2 = 36

The GCF × LCM Rule

For any two numbers $a$ and $b$ , there is a useful relationship between their GCF and LCM.

\text{GCF}(a, b) \times \text{LCM}(a, b) = a \times b

For example, with 12 and 18: $6 \times 36 = 216$ and $12 \times 18 = 216$ . This works because the Venn diagram accounts for every prime factor exactly once.