Factors, Prime Numbers, Prime Factors & Highest Common Factor (HCF)

In this video, it is clearly explained that the factors of a number are natural numbers that can be divided into the original number without a remainder. For example, the factors of 6 are 1; 2; 3; and 6. As 1 x 6 = 6, we can say that 1 and 6 is a factor pair of 6. The same with 2 and 3. They are also a factor pair of 6.

But what are prime numbers then? Prime numbers are numbers that only have one factor pair consisting of the number 1 and the original number. Take 7 as an example. The factors of 7 are 1 and 7. Thus, as there is only one factor pair, 7 is a prime number. Take note, that when listing prime numbers, 2 is the only even prime number. Why? 2 has only one factor pair consisting of 1 and itself. All the other even numbers are divisible by 2, so, they will all have more than one factor pair – making 2 the only even number that is a prime number.

How can we determine the prime factors of a certain number? Prime factors are the factors of a number that are also prime numbers. For example, as seen earlier, the factors of 6 are 1; 2; 3 and 6. However, which of those numbers are prime numbers? Only 2 and 3. So, the prime factors of 6 will be 2 and 3. To determine the highest common factor of two numbers, you have to write down all the factors of the two numbers and see which of those numbers are overlapping and which overlapped number is the biggest.