# 145 is not prime, is a composite number. 145 = 5 × 29; 144 = ? ... 146 = ?Explanations below.

## How to factor a number into prime factors (prime factorization)

Let's learn by an example, take the number 220 and build its prime factorization.

0) We need the first prime numbers list, let's say from 2 up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime numbers are the basic blocks when building the prime factorization of the composite numbers.

1) Start by dividing 220 by the first prime number, 2:
220 ÷ 2 = 110; remainder is zero => 220 is divisible by 2 => We've just calculated a prime factor of our number: 2. So, 220 = 2 × 110.

2) Divide the result of the previous operation, 110, by 2, again:
110 ÷ 2 = 55; remainder is zero => 110 is divisible by 2 => We've got yet another prime factor of our number: 2. So, 220 = 2 × 2 × 55.

3) Divide the result of the previous operation, 55, by 2, again:
55 ÷ 2 = 27 + 1; remainder is 1 => 55 is not divisible by 2.

4) Divide the result of the step 2 operation, 55, by the next prime number, 3:
55 ÷ 3 = 18 + 1; remainder is 1 => 55 is not divisible by 3.

5) Divide the result of the step 2 operation, 55, by the next prime number, 5:
55 ÷ 5 = 11; remainder is zero => 55 is divisible by 5 => We've got another prime factor of our number: 5. So, 220 = 2 × 2 × 5 × 11.

6) Notice that 11 is also a prime number, so we've got already all the prime factors of 220.

7) Conclusion: 220 prime factorization: 220 = 2 × 2 × 5 × 11.
This product of prime factors can be written in a condensed form, by the use of exponents: 220 = 22 × 5 × 11.

The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers in a way that is unique, except for the order of the prime factors.

1 is not considered prime, so the first prime number is 2. If 1 were admitted as a prime, number 15 for example could be prime factorized as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations, so the theorem above would have to be modified.

If a number is a prime, it can not be factored into other prime factors, it is divisible only by 1 and itself (called an IMPROPER FACTOR, or improper divisor). A composite number is also any positive integer larger than 1 that is not a prime number.

A composite number can be factored, as it is shown bellow:

Example 1: 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime, it's a composite number; 6 can be factored in different ways, as 1 × 6, or 1 × 2 × 3, or 2 × 3; but its prime factorization is always: 6 = 2 × 3.

Example 2: 120 can be factored in different ways, as 4 × 30 or 2 × 2 × 2 × 15 or 2 × 2 × 2 × 3 × 5; its prime factorization is always: 120 = 23 × 3 × 5; this is the condensed form of writing, with exponents, of the longer: 120 = 2 × 2 × 2 × 3 × 5.

## Latest factored numbers

 145 = 5 × 29 Oct 21 12:13 UTC (GMT) 90 = 2 × 32 × 5 Oct 21 12:13 UTC (GMT) 8,800 = 25 × 52 × 11 Oct 21 12:13 UTC (GMT) 371 = 7 × 53 Oct 21 12:13 UTC (GMT) 115 = 5 × 23 Oct 21 12:13 UTC (GMT) 300 = 22 × 3 × 52 Oct 21 12:13 UTC (GMT) 2 is a prime number Oct 21 12:13 UTC (GMT) 19 is a prime number Oct 21 12:13 UTC (GMT) 714 = 2 × 3 × 7 × 17 Oct 21 12:13 UTC (GMT) 3 is a prime number Oct 21 12:13 UTC (GMT) 266 = 2 × 7 × 19 Oct 21 12:13 UTC (GMT) 918 = 2 × 33 × 17 Oct 21 12:13 UTC (GMT) 123 = 3 × 41 Oct 21 12:13 UTC (GMT) see more... integer numbers factored down to their prime factors