Question

What is the GCF of 18 and 21 ?

Answer 1

Hint: The GCF which is a short form for Greatest Common Factor is the largest common factor of two or more than two numbers. Unlike the factors of a number, which is always a prime number, it can take any value. We will write the given numbers as the product of their factors and find all the common factors. The product of these common factors will give us the required GCF.

Complete step-by-step solution:
We have the given set of numbers as: 18 and 21 .
We will now write them as a product of their common factors. On doing so, we get the following equations:
$\Rightarrow 18=2\times 3\times 3$
Let us name the above equation as $(1)$, so we have:
$\Rightarrow 18=2\times 3\times 3$ ………$(1)$
And,
$\Rightarrow 21=3\times 7$
Let us name the above equation as $(2)$, so we have:
$\Rightarrow 21=3\times 7$ ………$(2)$
Now, collecting the common factors of 18 and 21 from equation number $(1)\text{ and (2)}$, we get the common factor as:
$\Rightarrow C.f.=3$
Here, we get only one common prime factor for 18 and 21. Thus, it will be the greatest common factor of the two numbers.
Hence, the Greatest Common Factor or GCF of 18 and 21 comes out to be 3.

Note: One should never misinterpret the term GCF with LCM as both of them have totally opposite meanings. LCM of a set of numbers is the least common multiple of the set of numbers. We can remember the difference as, GCF of a set of numbers is always less than the smallest number and LCM of a set of numbers is always greater than the largest number.