Prime Numbers are basically numbers that don't divide by anything but themselves and 1.
Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, etc.
Factors of a number are the integers (whole numbers) that divide into it without any remainders or decimals.
Factors can also be thought of as the times tables in which a number appears.
Every number have a finite amount of factors (numbers with exactly two factors are called the prime numbers).
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
The prime factors of a number are the factors which are also prime numbers. In the case of 36, 2 and 3 are its prime factors.
To write 36 as a product of its prime factors, we need a combination of 2 and 3 that we can multiply together to make 36. In this case it’s:
2 x 2 x 3 x 3
Try it. Guarantee it will make 36.
Every number can be written as a unique combination of prime numbers. Prime numbers are like the atoms, the indivisible building blocks, of numbers.
A common method for figuring out what combination of prime numbers you need, is to use something called a factor tree (sometimes referred to as prime factor decomposition).
This is best where you start at the top and split your number off into factors as shown:
Each time you get a prime you circle it and you finally end up with all the prime factors, which you can arrange in order.
420 = 2 x 2 x 3 x 5 x 7
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