Factor Calculator

Factor Calculator-Use our Factor Calculator to find all the factors of a number quickly and easily. You can also find factor pairs, prime factors, prime factorization, number of factors, and more.Convert units quickly with our free measurement and Rounding Calculator conversion calculators.

Simply enter a whole number and let the calculator do the work for you.

This tool is useful for students, teachers, parents, and anyone who wants to check a math problem without spending a lot of time finding factors by hand.

What Is a Factor?

A factor is a whole number that divides another number exactly, with no remainder.

For example, the factors of 12 are:

1, 2, 3, 4, 6, 12

Each of these numbers divides 12 evenly.

For example:

• 12 ÷ 1 = 12
• 12 ÷ 2 = 6
• 12 ÷ 3 = 4
• 12 ÷ 4 = 3
• 12 ÷ 6 = 2
• 12 ÷ 12 = 1

So all of these numbers are factors of 12.

A factor is sometimes also called a divisor.

What Is a Factor Calculator?

A Factor Calculator is an online math tool that finds the factors of a number automatically.

Depending on the calculator, it can show:

• All factors
• Factor pairs
• Prime factors
• Prime factorization
• Factor tree
• Number of factors
• Sum of factors
• Proper factors
• Prime or composite status
• Greatest common factor (GCF)

These are common uses of factor calculators today.

Instead of checking every number yourself, you can enter your number and get the answer in seconds.

How to Use the Factor Calculator

Using our online Factor Calculator is simple.

Step 1: Enter a number

Enter the whole number you want to factor.

For example:

60

Step 2: Click Calculate

The calculator checks the number and finds its factors.

Step 3: View the results

You can see the complete factor list, factor pairs, prime factorization, and other useful information.

For example, the factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The prime factorization is:

60 = 2² × 3 × 5

Factors of a Number

To find the factors of a number, look for whole numbers that divide the number without leaving a remainder.

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24

You can check them like this:

1 × 24 = 24

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

This also gives us the factor pairs.

Factor Pairs

A factor pair consists of two numbers that multiply together to give the original number.

For example, the factor pairs of 24 are:

• 1 × 24
• 2 × 12
• 3 × 8
• 4 × 6

Every pair gives 24.

Factor pairs are useful because they make it easier to find all the factors of a number.

Example: Factor Pairs of 36

The factor pairs of 36 are:

1 × 36

2 × 18

3 × 12

4 × 9

6 × 6

Therefore, the factors of 36 are:

1, 2, 3, 4, 6, 9, 12, 18, 36

Prime Factorization

Prime factorization means breaking a number down into prime numbers that multiply together to make the original number.

For example:

60 = 2 × 2 × 3 × 5

Using exponents:

60 = 2² × 3 × 5

The numbers 2, 3, and 5 are prime numbers.

Every whole number greater than 1 has a unique prime factorization.

Prime Factorization Example

Let’s find the prime factorization of 72.

Start by dividing by 2:

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

Now divide by 3:

9 ÷ 3 = 3

3 ÷ 3 = 1

So:

72 = 2 × 2 × 2 × 3 × 3

Or:

72 = 2³ × 3²

Therefore, the prime factorization of 72 is 2³ × 3².

Prime Factors

Prime factors are the prime numbers that divide a number exactly.

For example, the prime factorization of 30 is:

30 = 2 × 3 × 5

Therefore, the prime factors of 30 are:

2, 3, and 5

A number can have many factors but only a smaller set of prime factors.

For example, 60 has 12 positive factors, but its prime factors are only:

2, 3, and 5

Prime Factorization Calculator

A Prime Factorization Calculator breaks a number into its prime factors automatically.

For example, enter:

120

The calculator can show:

120 = 2³ × 3 × 5

This can be much faster than creating a factor tree by hand.

Prime factorization is useful in many areas of math, including finding GCF, LCM, simplifying fractions, and working with divisibility.

Factor Tree

A factor tree is a visual way to break a composite number into prime numbers.

For example, let’s factor 36.

Start with:

36

Break it into:

4 × 9

Then break those numbers down:

4 = 2 × 2

9 = 3 × 3

So the prime factors are:

2 × 2 × 3 × 3

Therefore:

36 = 2² × 3²

A factor tree is especially helpful for students because you can see how the original number is broken into smaller factors.

Number of Factors Calculator

A Number of Factors Calculator tells you how many positive factors a number has.

For example, 12 has these factors:

1, 2, 3, 4, 6, 12

So 12 has:

6 factors

You can also find the number of factors from prime factorization.

For example:

60 = 2² × 3¹ × 5¹

Add 1 to each exponent:

(2 + 1)(1 + 1)(1 + 1)

= 3 × 2 × 2

= 12

Therefore, 60 has 12 positive factors.

How to Find the Factors of a Number

You can find factors manually by checking which numbers divide the original number without a remainder.

Start with 1:

1 × 48 = 48

Then:

2 × 24 = 48

3 × 16 = 48

4 × 12 = 48

6 × 8 = 48

So the factors are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

You do not need to check every number all the way to 48. Once you reach the square root, the remaining factors appear as the matching partners of the smaller factors.

Factors of 100

The factors of 100 are:

1, 2, 4, 5, 10, 20, 25, 50, 100

The factor pairs are:

• 1 × 100
• 2 × 50
• 4 × 25
• 5 × 20
• 10 × 10

The prime factorization is:

100 = 2² × 5²

So 100 has 9 positive factors.

Factors of 50

The factors of 50 are:

1, 2, 5, 10, 25, 50

Factor pairs:

• 1 × 50
• 2 × 25
• 5 × 10

Prime factorization:

50 = 2 × 5²

Factors of 36

The factors of 36 are:

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor pairs:

• 1 × 36
• 2 × 18
• 3 × 12
• 4 × 9
• 6 × 6

Prime factorization:

36 = 2² × 3²

Factors of 24

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24

Factor pairs:

• 1 × 24
• 2 × 12
• 3 × 8
• 4 × 6

Prime factorization:

24 = 2³ × 3

Factors of 12

The factors of 12 are:

1, 2, 3, 4, 6, 12

Factor pairs:

• 1 × 12
• 2 × 6
• 3 × 4

Prime factorization:

12 = 2² × 3

Greatest Common Factor (GCF)

The Greatest Common Factor, or GCF, is the largest factor that two or more numbers have in common.

It is also called the Greatest Common Divisor (GCD).

For example, find the GCF of 12 and 18.

Factors of 12:

1, 2, 3, 4, 6, 12

Factors of 18:

1, 2, 3, 6, 9, 18

The common factors are:

1, 2, 3, 6

The largest one is:

6

Therefore:

GCF(12, 18) = 6

A factor calculator can be combined with a GCF calculator to solve these problems more quickly.

Factors vs. Multiples

Factors and multiples are related, but they are not the same thing.

Factors

Factors divide a number exactly.

For example, the factors of 10 are:

1, 2, 5, 10

Multiples

Multiples are created by multiplying a number by whole numbers.

The multiples of 10 are:

10, 20, 30, 40, 50, …

An easy way to remember the difference is:

Factors divide. Multiples multiply.

Prime Numbers vs. Composite Numbers

A prime number has exactly two positive factors:

1 and itself

Examples include:

2, 3, 5, 7, 11, 13

A composite number has more than two positive factors.

Examples include:

4, 6, 8, 9, 10, 12

For example:

7

Factors:

1, 7

So 7 is prime.

But:

12

Factors:

1, 2, 3, 4, 6, 12

So 12 is composite.

The number 1 is neither prime nor composite because it has only one positive factor.

Proper Factors

A proper factor is a factor other than the number itself.

For example, the factors of 12 are:

1, 2, 3, 4, 6, 12

The proper factors are:

1, 2, 3, 4, 6

The number 12 is not included.

Proper factors can also be used to classify numbers as perfect, deficient, or abundant.

Perfect, Abundant and Deficient Numbers

Factors can tell us more about a number.

Perfect Number

A perfect number is a number whose proper factors add up to the number itself.

For example:

6

Proper factors:

1, 2, 3

Their sum is:

1 + 2 + 3 = 6

So 6 is a perfect number.

Abundant Number

A number is abundant when the sum of its proper factors is greater than the number.

For example, 12:

1 + 2 + 3 + 4 + 6 = 16

Since 16 is greater than 12, 12 is abundant.

Deficient Number

A number is deficient when the sum of its proper factors is less than the number.

For example, 8:

1 + 2 + 4 = 7

Since 7 is less than 8, 8 is deficient.

Why Use an Online Factor Calculator?

Finding factors of small numbers by hand is easy.

But larger numbers can take more time.

A free online Factor Calculator can help you:

• Find all factors quickly
• Find factor pairs
• Find prime factors
• Get prime factorization
• Check whether a number is prime
• Count the number of factors
• Create or understand a factor tree
• Check your homework
• Find GCF-related information
• Avoid simple calculation mistakes

It is especially useful when you are working with large numbers or checking several problems.

Who Can Use a Factor Calculator?

Students

Students can use it for math homework, worksheets, classwork, and exam preparation.

Teachers

Teachers can use it to check examples and explain factorization to students.

Parents

Parents can use it when helping children learn factors, multiples, primes, and divisibility.

Anyone Learning Math

You do not need advanced math knowledge to use a factor calculator. Enter the number and review the results.

Factor Calculator Example

Let’s factor 72.

First, find the factor pairs:

1 × 72

2 × 36

3 × 24

4 × 18

6 × 12

8 × 9

Therefore, the factors are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Now find the prime factorization:

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Therefore:

72 = 2³ × 3²

The number has:

12 positive factors

Frequently Asked Questions

What is a factor calculator?

A Factor Calculator is an online tool that finds the factors of a number. It can also show factor pairs, prime factorization, prime factors, factor count, and other number properties.

How do I find all factors of a number?

Check which whole numbers divide the number without a remainder. Every successful divisor has a matching factor. For larger numbers, a calculator can find the complete list quickly.

What is the factor of a number?

A factor is a whole number that divides another number exactly with no remainder.

What is a factor pair?

A factor pair is two numbers that multiply together to give the original number.

For example:

3 × 8 = 24

So 3 and 8 are a factor pair of 24.

What is prime factorization?

Prime factorization breaks a number into a product of prime numbers.

For example:

60 = 2² × 3 × 5

What is a prime factor?

A prime factor is a prime number that divides the original number exactly.

What is a factor tree?

A factor tree is a visual method for breaking a composite number into prime factors.

How many factors does 12 have?

12 has six positive factors:

1, 2, 3, 4, 6, 12

Is 1 a prime number?

No. The number 1 has only one positive factor, so it is neither prime nor composite.

What is the difference between a factor and a multiple?

A factor divides a number exactly. A multiple is the result of multiplying a number by a whole number.

Can a factor calculator find prime numbers?

Yes. If a number has exactly two positive factors, 1 and itself, it is prime.

Can I use a factor calculator for large numbers?

Yes, depending on the calculator’s input limit. Larger numbers may require more computation, especially when finding complete factor lists.

What is the GCF?

GCF means Greatest Common Factor. It is the largest positive factor shared by two or more numbers.

What is the GCD?

GCD means Greatest Common Divisor. It is another name for the Greatest Common Factor (GCF).

Final Thoughts

Finding factors is an important part of basic math, but checking a large number by hand can take time.

Our Factor Calculator makes it easier to find all factors, factor pairs, prime factors, prime factorization, factor trees, factor count, proper factors, and more.

Whether you are checking homework, learning prime factorization, finding a GCF, or simply trying to understand the factors of a number, CalculatorGuides.com gives you a quick and simple way to get the answer.