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:
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.
When two natural numbers are multiplied to result in a number, then the two numbers being multiplied are termed as the factors of the product.
A composite number is a number that has factors other than 1 and itself. Hence, a composite number has more than two factors.
Prime numbers are those numbers which have only 2 factors, 1 and the number itself.
When any number is divided by 1, we get the remainder as 0 and the quotient as the number itself. Hence, 1 is a factor of all numbers.