Question

How do you find the GCF of 9 and 15 and 24?

Answer 1

Hint: In the above question we were asked to find the Greatest Common Factor of 9, 15, and 24. GCF or HCF is different from LCM. In a GCF or HCF, you have to find common factors of the numbers, the largest of common factors among those numbers are called GCF.

Complete Step by Step Solution:
In the given question we have to find the GCF of 9, 15, and 24. So we will first find out the prime factors of all these three numbers.
$\Rightarrow 9\text{ }=\text{ }3\text{ }\times \text{ }3$
$\Rightarrow 15\text{ }=\text{ }3\text{ }\times \text{ }5$
$\Rightarrow 24\text{ }=\text{ }2\text{ }\times \text{ }2\text{ }\times \text{ }2\text{ }\times \text{ }3$
The above are the factors of 9, 15, and 24. So, let us see what the Greatest Common Factor among them,
As you can see, there are two 3s in 9 but one 3 in 15 and 24. So, 3 will be a common factor.
In 15, except 3 there is one 5 but not in 9 or 24. So, 5 cannot be a common factor.
In 24 there are three 2s and one 3 but there are no two in 9 or 15.

Therefore, GCF or 9, 15, and 24 are 3.

Note:
In the above solution, we solved GCF of 9, 15, and 24. We found only one common factor that is 3 and it is also the highest factor so we considered it as GCF. The GCF is the highest number that is shared between two numbers but an LCM is an integer shared by two numbers that are divisible by both numbers.