Question

What are the common factors of 24 and 36?

Answer 1

Hint: To obtain the common factors of the numbers given we will find the factors of each number. Firstly we write the numbers that divide the given numbers completely without leaving any remainder. Then we will check out the factors that are common in both the numbers and finally we will get the desired answer.

Complete step by step solution:
The numbers given are as follows:
$24,36$
Firstly we will find factors of number 24 as:
$24=\left\{ 1,2,3,4,6,8,12,24 \right\}$…..$\left( 1 \right)$
Next the factors of the number 36 are:
\[36=\left\{ 1,2,3,4,6,9,12,18,36 \right\}\]…..$\left( 2 \right)$
We can see that in both equation (1) and (2) all the factors inside the bracket completely divide the numbers.
On comparing equation (1) and (2) we get the common factors as below:
$\left\{ 1,2,3,4,6,12 \right\}$
Hence the common factors of 24 and 36 are $\left\{ 1,2,3,4,6,12 \right\}$

Note: A number that divides another number without leaving any remainder is known as its factor. Also we can say that when any integer is multiplied with the integer $b$ to produce some integer $c$ then $b$ is known as factor of $c$. The number 1 and -1 divides every integer and every integer is a factor of itself. Prime factorization is when we write the numbers as a product of prime numbers the numbers might repeat. A factor is always a whole number or an integer but it can never be a fraction or a decimal value. Common factors also help in finding out the H.C.F of the numbers which is the highest common factor among them.