Factors and Primes

This chapter explores factors and primes. It explores finding factors of numbers, finding highest common factors and finding prime numbers. No prior knowledge is required for this chapter.

What is a factor?

A factor is a number which divides exactly into another number for example to find the factors of 20.

…that means 20 is a factor of 20.

…2 and 10 is a factor of 20.

…that means 5 and 4 is a factor of 20.
So the factors of 20 are;

By now you know that a number which divides exactly into another number with no remainders is called a factor of that number.
Suppose we wanted to list the factors of 16; You solve this by dividing 16 by 1,2,3,etc.

The factors of 36 are;

The factors of 100 are;

Highest Common factors

The highest common factor (HCF) is the biggest number which can be divided by both numbers in the list without any remainders. Suppose we wanted to find the highest common factor of 18 and 30.
First we list the factors of 18;

Then we list the factors of 30.

The biggest number in both lists is 6.

…this number has been circle above. We say that the highest common factors of 18 and 30 is 6.

Prime numbers

Prime numbers have only two factors that is themselves and the number 1.
Below is a list of prime numbers up to 100;

Finding prime factors

When asked to find prime factors of a number simply list all the factors of that number and circle the numbers which are prime numbers, for example;
Suppose we wanted to find the prime factors of 48. First we list down all the factors of 48.

Then we circle the prime numbers.

The prime factors of 48 are; 2 and 3.
Suppose we wanted to find the prime factors of 25. First we list all factors of 25;

…then we circle the prime numbers.

The prime factors of 25 is only 5.
How about the prime factors of 17. First we list all factors of 17;

…then circle the prime numbers

The prime numbers of 17 is only 17.