The value entered is the prime factorization.

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## Prime factorization

## About calculating prime factorization

Enter the number of factoring and click the button "Calculate factoring", displays the value you entered is prime factorization.

The factorized values are displayed in multiplication form, exponential form, and a list of prime factors.

Please enter an integer between 2 and 10,000,000,000,000,000.

## What is prime factorization?

Prime factorization is the process of breaking down a positive integer into a product of prime numbers.

A prime number is a natural number greater than 1 that has no other divisors than 1 and itself.

A natural number greater than 1 that has no divisors other than 1 and itself is called a composite number.

For example, the number 5 is a prime number because its only divisors are 1 and 5.

However, the divisors of 6 are 1, 2, 3, and 6, making it a composite number since it has other divisors besides 1 and 6.

If a number has a divisor other than 1 and itself, you can express it as a product of smaller numbers by dividing it by that divisor.

In the case of 36, it can be expressed as 36 = 3 × 12. Furthermore, 12 can be expressed as 2 × 6.

Decomposing a number in this way and turning it into a product of all prime numbers is called prime factorization.

## How to factorize a number

When calculating a prime factorization, you divide the number by smaller prime numbers until it is no longer divisible by them.

Finally, when the quotient becomes a prime number and can no longer be divided, it is expressed as a product.

### Calculation example

Factorize 120 into prime integers.

90 is divisible by 2, so the result is 90÷2 = 45.

45 is divisible by 3, so the result is 45÷3 = 15.

15 is divisible by 3, so the result is 15÷3 = 5.

Since the quotient is 5, which is a prime number, we can multiply the quotient and the divided number to give us 90 = 2 × 3 × 3 × 5, which can be factorized as prime factorization.

#### Prime factorization by long division

To find the prime factorization of a number, you can do it easily by calculating it by hand.

Write the number you want to factorize and then write the number to the left of it.

2 | 90 | |

Write the quotient when you divide the first number by the number on the left underneath the first number.Keep calculating until you can no longer divide it.

2 | 90 | |

3 | 45 | |

3 | 15 | |

5 |

When it is no longer divisible, multiply the number on the left and the final quotient to get 2 × 3 × 3 × 5, which can be decomposed into prime factors.

- ･Prime factorization
- ･Greatest common divisor (two numbers)
- ･Greatest common divisor (three numbers)
- ･Divisor
- ･Common divisor (two numbers)
- ･Common divisor (three numbers)
- ･Least common multiple (two numbers)
- ･Least common multiple (three numbers)
- ･Common multiple (two numbers)
- ･Common multiple (three numbers)