Factor Calculator | Free Online Factor Calculator with Steps - BYJUS

# Factor Calculator

The factor calculator is an online free tool that can be used to factor a number. Let us get familiar with the calculator....Read MoreRead Less

## Online Factor Calculator

### How do we use the Factor Calculator?

Follow the steps below to use the factor calculator:

Step 1: Enter a number into the input box and the prime factorization of the number will be displayed.

Step 2: Click on the ‘Solve’ button to obtain the result.

Step 3: Click on the ‘Show Steps’ button to view the stepwise solution applied to find the factored form of the number.

Step 4: Click on the button to enter new inputs and start again.

Step 5: Click on the ‘Example’ button to play with different random input values.

Step 6: Click on the ‘Explore’ button to visualize the factoring of a number.

Step 7: When on the ‘Explore’ page, click the ‘Calculate’ button, if you want to go back to the calculator.

### What is a factor?

The factors of a number are natural numbers that divide the given number completely. In other words, when a number is divided by its factors the remainder is 0.

Let’s take a look at a few representations of factoring a number:

Prime Factorization

The factors of a number that are prime numbers are called the prime factors of that number. The method of expressing a number as a product of its prime factors is called prime factorization.

Factor Tree

A factor tree is a method of expressing the factors of a number similar to the branches of a tree. A factor tree helps us visualize the prime factorization of a number. In this method we continuously divide the number by its prime factors. With each step of the division operation, a branch is added to the factor tree. The division is continued till we get the quotient as 1.

Factor Pairs

The factor pair of a number is a set of two factors of the number that when multiplied together results in the number itself.

### Solved Examples

Example 1: Using a factor tree, demonstrate the prime factorization of 120.

Solution:

Therefore, the prime factorization of 120 is 2 $$\times$$ 2 $$\times$$ 2 $$\times$$ 3 $$\times$$ 5

Example 2: Derive the factor pairs of 40, and list the factors of 40.

Solution:

 Multiplication Equation Factor pairs 1 $$\times$$ 40 = 40 (1, 40) 2 $$\times$$ 20 = 40 (2, 20) 4 $$\times$$ 10 = 40 (4, 10) 5 $$\times$$ 8 = 40 (5, 8) 8 $$\times$$ 5 = 40 (8, 5) 10 $$\times$$ 4 = 40 (10, 4) 20 $$\times$$ 2 = 40 (20, 2) 40 $$\times$$ 1 = 40 (40, 1)

Therefore the factors of 40 are: 1, 2, 4, 5, 8, 10, 20 and 40.

Example 3: Check if 11 is a factor of 89.

Solution:

The rule is that, a number divided by its factor, results in a remainder of 0.

Hence, $$\frac{89}{11}=8 R1$$

89 divided by 11, results in a quotient of 8 and a remainder of 1.

Since the remainder is not 0, 11 is not a factor of 89.