Prime Factorization

Prime Number

• A natural number greater than 1 that is not a product of two smaller natural numbers.
• A positive integer greater than 1 that can only be divided by itself and 1 without leaving a remainder.
• A prime number is a whole number greater than 1 whose only factors are 1 and itself.
• A number that cannot be divided by any other number except itself and the number.
• A prime number is a positive integer that has exactly two positive divisors, 1 and it self.
• Examples: 2, 3, 5, 7, 11, ... One (1) is not a prime number.

Composite Number

• is a natural number with more than two factors.

Suggested Solution:

1. Using divisibility rules check the given number if it is divisible by prime numbers (start with the lowest) (2, 3, 5, 7, 11, 13, 17, 19, 23, ...)
2. If possible divide the number by that prime number
3. Repeat process to the quotient until the remaining quotient is a prime number.
Note: If you're using the factor tree this solution is a good one. It is a bad idea to start a factor tree by dividing large numbers - although this is not wrong but dividing large number is quite difficult to do compared to dividing smaller numbers, but you can do it it's not a problem.

Examples

1. Find the prime factors of 100.
100 is divisible by 2
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5, since the last quotient is 5, a prime number stop here.




Thus the prime factors of 100 = 2 x 2 x 5 x 5

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2. Find the prime factors of 15, 975.
15, 975 is divisible by 5
15, 975 ÷ 5 = 3195
3195 ÷ 5 = 639
639 ÷ 3 = 213
213 ÷ 3 = 71




Thus the prime factors of 15, 975 = 5 x 5 x 3 x 3 x 71