FACTORS OF 24 AND HOW TO FIND THEM

WHAT ARE THE FACTORS OF 24

Factors are the numbers that completely divide the original number and leave no remainder. The factors of 24 are the numbers that will divide 24 completely and leave no remainder whatsoever. The numbers that divide 24 completely (factors) are 1, 2, 3, 4, 6, 8, 12 and 24.

They can be written in ordered pairs as follows:

Factors of a number can be prime numbers or composite numbers. What are prime numbers? Prime numbers are those numbers that have only two factors which are 1 and the number itself whereas composite numbers are those that have more than two factors.

For example, 31 is a prime number because it has only two factors and is written as 31 = 1 x 31

47 is a prime number as it has only 1 and 47 as its factors. 47 = 1 x 47

6 is a composite number as it has more than two factors which are 1, 2, 3 and 6.

6 = 1 x 6 , 6 = 2 x 3

36 is a composite number as it has more than two factors : 1, 2, 3, 4, 6, 9, 12, 18, 36

1 x 36 = 36, 2 x 18 = 36, 3 x 12 = 36, 4 x 9 = 36, 6 x 6 = 36

HOW TO FIND THE FACTORS OF 24?

We will find all the numbers the product of which gives us the answer as 24. All these numbers will be the factors of 24. We can start with 1 and continue till 24 to see which all numbers completely divide 24 and give us whole numbers as answers with no remainders.

This will give us the factors of 24 which are:

FACTORS OF 24 BY PRIME FACTORIZATION METHODS

Prime factorization is simply expressing or breaking down a composite number as a product of its prime factors. Now we will understand the concept of finding the factors using prime factorization. There are two methods by which we can find the prime factors. We can either use the prime factorization by the long division method or the factor tree method.

1. Prime factorization by factor tree method

We take the number 24 as the root of the tree and the factors as branches. We keep on breaking the composite numbers till we have only prime numbers left.

So prime factorization of 24 is 24 = 2 x 2 x 2 x 3 or simply put 24 = 2³ x 3

2. Long division method

This method starts with dividing the original number with the smallest prime number possible and then keeps on dividing the quotient we get each time till the remainder is 1. Let us see how it is done:

We arrive at the same answer as the factor tree method and get 24 = 2³ x 3.