Factors of Numbers

Factors of a number are nothing but the numbers you multiply together to get a number. Put simply, for example, in the number 15, the factors are 3 and 15, because when you multiply 3 and 5 you get 15, 3×5=5. But remember some numbers have more than two factors.

For example, take the number 12, it can be derived in multiple ways, like 3×4=12, 2×6 = 12 and even 1×12=12, so the factors here are 1,2,3,4 and 6. Factors are whole numbers, hence you cannot count in fractions ½ x 6 =3, but ½ cannot be included as a factor of 3, because it is not a whole number.

Factoring Numbers: Prime Factorization

You may also need to frequently find the prime factors of a number. Prime factorizations are nothing but factors of a number that include only prime numbers. Let’s take the number 8, the factors for the number may include 1×8=8, 2×4 = 8, so the factors are 1,2,4,8 but the prime number here is only 2, since the number 1 is not regarded as a prime number. So, the prime factor of number 8 is only 2.

Even though 2×4=8 and 4 is a factor of that number, it is not considered in prime factorization as only prime numbers are considered. The reason behind this is 8=2x2x2 but when you include 4 it will become something like 2x2x2x4 which is not equal to 8. This is mainly done to avoid the over-duplication of factors and that is the reason prime factorization is one of the best fool-proof methods.

Let’s take another example to find the prime factorization of 24.

The factors for 24 are 1,2,3,4,6,12 and 24 because 2x3x4 = 24, 2×12 = 24, 6×4 =24, 1×24=24. But when it comes to the prime factorization of 24, we cannot simply include all the factors as it will lead to multiplying all numbers such as 2x3x4x5x12x24 which is equal to 331776 and this is completely wrong.

But when you take just the prime numbers, they are 2 and 3, so that when you multiply 2x2x2x3 = 24 which is correct. Hence the prime factors for 24 are 2 and 3 and the prime factorization is 24-2x2x2x3.

Another easy way of finding the factors is doing upside-down division. Let’s take the following example, 24 again. When you look at the image below, you can work out how to calculate the factors of a number quite easily.

Factors of Numbers