Factors of a positive integer n are all the positive integers that divide n with remainder equal to zero.
For example 2, 3, 4 and 6 are factors of 12 since
12 / 2 = 6, 12 / 3 = 4, 12 / 4 = 3 and 12 / 6 = 2.
These factors are also present when 12 is written as a product of factors (factoring).
For example 12 = 6 . 2, 12 = 4 . 3 ...
The fundamental theorem of arithmetic states that there is only one way that a given positive integer can be represented as a product of one or more primes numbers.
A Prime number n is a positive integer greater than 1 that has only 1 and n (itself) as positive integer divisors.
Below is a list of the first prime numbers
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,...
How to find prime Factors of a positive integer?
We start by dividing the given number by 2 if possible, then divide the result by 2 if possible; if not divide by the next prime number 3 and continue until the quotient is a prime number
Example 1: Factor 4 into prime numbers
Solution
4 = 2 . 2 = 2 2
Example 2: Factor 20 into prime numbers
Solution
step 1. 20 = 2 . 10
step 2. 20 = 2 . 2 . 5
20 = 2 . 2 . 5 = 2 2 . 5
Example 3: Factor 100 into prime numbers
Solution
step 1. 100 = 2 . 50
step2. 100 = 2 . 2 . 25
step3. 100 = 2 . 2 . 5 . 5
100 = 2 . 2 . 5 . 5 = 2 2 . 5 2
Example 5: Factor 1020 into prime numbers
Solution
step 1. 1020 = 2 . 510
step 2. 1020 = 2 . 2 . 255
step 3. 1020 = 2 . 2 . 3 . 85
step 4. 1020 = 2 . 2 . 3 . 5 . 17
1020 = 2 . 2 . 3 . 5 . 17 = 2 2 . 3 . 5 . 17
Example 6: Factor 634 into prime numbers
Solution
step 1. 634 = 2 . 317
634 = 2 . 317
Example 7: Factor 720 into prime numbers
Solution
step 1. 720 = 2 . 360
step 2. 720 = 2 . 2 . 180
step 3. 720 = 2 . 2 . 2 . 90
step 4. 720 = 2 . 2 . 2 . 2 . 45
step 5. 720 = 2 . 2 . 2 . 2 . 3 . 15
step 6. 720 = 2 . 2 . 2 . 2 . 3 . 3 . 5
720 = 2 4 . 3 2 . 5
More on numbers and Fractions.