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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.

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