Positive Factors, Prime Factors and HCF

Factors: TO HELP YOU UNDERSTAND FACTORS, LETS FORGET THAT DECIMALS AND FRACTIONS EXIST, JUST THIS ONCE!

Factors are positive or negative integers. They are integers, this means the number can be positive or negative but cannot be a decimal or a fraction. For example, -1 can be a negative factor, 2 can be a positive factor, however, -1.5 and 9.5 are not factors as they are decimals.
Lets explain positive factors by giving an example. The number 18 can be divided by a certain amount of positive integers which gives integers as answers. These numbers are 1, 18, 2, 3, 6 and 9. These numbers are the positive factors of 18.
Is 5 a factor of 18? NO, because even though it is possible to divide 18 by 5 which gives 3.6, 3.6 is a decimal not an integer, so that is why 5 is not a factor of 18.
18/1 = 18 (answer, 18, is a positive integer so 1 is a positive factor)18/18 = 1 (answer, 1, is a positive integer, so 18 is a positive factor)18/2 = 9 (answer, 9, is a positive integer, so 2 is a positive factor)18/3 = 6 (answer, 6, is a positive integer, so 3 is a positive factor)18/6 = 3 (answer, 3, is a positive integer, so 6 is a positive factor)18/9 = 2 (answer, 2, is a positive integer, so 9 is a positive factor)

Lets explain negative factors by using the same example. The number 18 can be divided by a certain amount of negative integers which gives integers as answers. These numbers are -1, -18, -2, -3, -6, and -9.
18/-1 = -18 (answer, -18. is a negative integer, so -1 is a negative factor)18/-18 = -1 (answer, -1, is a negative integer, so -18 is a negative factor)18/-2 = -9 (answer, -9, is a negative integer, so -2 is a negative factor)18/-3 = -6 (answer, -6, is a negative integer, so -3 is a negative factor)18/-6 = -3 (answer, -3, is a negative integer, so -6 is a negative factor)18/-9 = -2 (answer, -2, is a negative integer, so -9 is a negative factor)
So another way to interpret factors is, if we have a number, and we want to know its positive or negative factors, we have to identify all the positive and negative integers, so that when we divide that number by those positive and negative integers, each answer is an integer.
When we focus on prime factors below, you will see that we focus on positive factors only.

Prime Factors:

These are factors which are prime numbers. We have gone through prime numbers in the prime numbers page. When we look at the factors of 18, we can see that the only prime numbers are 2 and 3. When we want to know the prime factors of a number, we need to look at the positive factors only. This is because prime numbers are numbers bigger than 1, which can be only be divided by itself and 1.

HCF (Highest Common Factor):

Now that we know what a factor is, lets say we have two or more numbers, for example, we have 18 and 32. We want to know each of their factors (we already know 18's factors) and find out the biggest factor they have in common. This factor is known as the HCF. Check out the HCF and LCM page to find out how to answer these questions.

Try answering these questions:

What are all the positive factors of 24?
Which of these factors in question 1 are prime numbers?

Answers:

24, 2, 12, 3, 8, 4, and 6
2 and 3.

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