Question

The common factors of $18$ and $24$ are $1,2,3,6$ .
a). True
b). False

Answer 1

Hint: In this question we have to check whether the given statement is true or false. So we will first write down all the factors of $18$ and then we find all the factors of $24$ . After that we will check if the given numbers have the same factors or not. We will also understand the definition of factor and common factor.

Complete step-by-step solution:
We know that when a number is multiplied with another number and gives the given number as result then we say that the number which we multiplied is the factor.
Now let us understand the definition of common factor:
They can be defined as the factors which can have the same factor for two or more numbers, then these factors are termed as common factors.
Here we have two numbers
$18,24$ .
We will find the factors of both numbers separately.
Let us find the find the factors of $18$ , they are
 $1,2,3,6,9,18$ .
We know that $1$ and the number itself are also the factors of the given numbers.
Now we have $24$, so the factors are:
$1,2,3,4,6,8,12,24$
We will now compare and find the numbers that are the same in both factors.
By comparing we have common factors as
$1,2,3,6$
So we can see that the given statement in the question is correct.
Hence the correct option is (a) True.

Note: We should note some of the important properties of factors. Such factors should note be greater than the given number. It should be less than or equal to the given.
We should note that every number has minimum two factors i.e.
$1$ and the number itself. These are the basic factors for every number.
So we can also say that $1$ is a common factor of all sets.