Factor Calculator

This factor calculator finds all factors of a number, prime factors, factor pairs, and checks if a number is prime. In advanced mode, it also calculates the Greatest Common Factor (GCF), Least Common Multiple (LCM), and common factors of two numbers.

Factors: All integers that divide evenly into a number.
Prime factors: Basic building blocks of the number’s multiplication.
Factor pairs: Two numbers multiplied together to make the original number.
Prime check: Instantly see if a number is prime or composite.
GCF & LCM: Find the greatest shared factor and smallest shared multiple for two numbers.

How to use: Enter one number to see its factors, prime factors, and factor pairs. Switch to advanced mode to enter two numbers and calculate GCF, LCM, and shared factors instantly.

Common searches: factor calculator online, prime factor calculator, factor pairs of a number, GCF and LCM calculator, prime check tool.

Find factors, prime factors, factor pairs, GCF, and LCM for one or two numbers.

What are factors?

Factors are numbers that divide another number exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Each of these numbers divides 12 evenly.

What are factor pairs?

A factor pair is a set of two numbers that multiply to make the original number. For 12, the factor pairs are 1 × 12, 2 × 6, and 3 × 4.

What are prime factors?

Prime factors are the basic building blocks of a number, expressed only with prime numbers. The prime factorization of 12 is 2 × 2 × 3. Breaking numbers down into prime factors helps with simplifying fractions and solving GCF or LCM problems.

Prime vs composite numbers

A prime number has exactly two factors: 1 and itself. Examples include 2, 3, 5, 7, 11. A composite number has more than two factors. For example, 12 is composite because it has six factors.

Number	Type	Factors
7	Prime	1, 7
12	Composite	1, 2, 3, 4, 6, 12

What is the Greatest Common Factor (GCF)?

The GCF is the largest number that divides two or more numbers evenly. For example, the GCF of 12 and 18 is 6 because 6 is the biggest factor they share.

What is the Least Common Multiple (LCM)?

The LCM is the smallest number that is a multiple of two or more numbers. For example, the LCM of 12 and 18 is 36 because 36 is the smallest number divisible by both 12 and 18.

Worked examples

Factors of 28: 1, 2, 4, 7, 14, 28
Prime factorization of 28: 2 × 2 × 7
GCF of 28 and 42: 14
LCM of 28 and 42: 84

Factor Calculator FAQs

1. What are factors in mathematics?Factors are whole numbers that divide another number evenly without leaving a remainder. For example, the factors of 16 are 1, 2, 4, 8, and 16.

2. What is the difference between factors and multiples?Factors are numbers that divide evenly into another number, while multiples are the results of multiplying a number by whole numbers. For example, the factors of 6 are 1, 2, 3, and 6, while the multiples of 6 include 6, 12, 18, and 24.

3. How do you find factors quickly?You can find factors quickly by dividing the number by integers starting from 1 up to its square root. Each time a number divides evenly, both the divisor and quotient are factors.

4. What are prime factors?Prime factors are factors of a number that are prime numbers. For example, the prime factorization of 30 is 2 × 3 × 5. Prime factors are useful for simplifying fractions, finding GCF, and calculating LCM.

5. How do you know if a number is prime?A number is prime if it has exactly two factors: 1 and itself. For example, 7 is prime because only 1 and 7 divide evenly into it. If a number has more than two factors, it is composite.

6. What is the Greatest Common Factor (GCF)?The GCF is the largest factor that two or more numbers have in common. For example, the GCF of 18 and 24 is 6.

7. What is the Least Common Multiple (LCM)?The LCM is the smallest number that is a multiple of two or more numbers. For example, the LCM of 5 and 6 is 30.

8.Why are factors important in math?Factors are important because they are used in simplifying fractions, solving algebra equations, finding divisibility, and working with GCF and LCM in real-life problems such as scheduling and ratios.