Question

What is the GCF of \[15\] and \[100\]?

Answer 1

Hint: We are asked to find out the GCF of \[15\] and \[100\]. In order to find it, firstly, we have to list out all the factors of both \[15\] and \[100\]. After listing them, we must check for the factor that is the highest and as well as the common factor which means it exists in both of the lists of factors. That factor would be our required answer.

Complete step by step solution:
Now let us learn about the Greatest Common Factor (GCF). It is the greatest factor that divides both the numbers. The GCF can be found in two methods. If there exists no common factor for two numbers, then the GCF of such a pair of numbers is one.
Now let us start finding out the GCF of \[15\] and \[100\].
Firstly, let us write down all the factors of \[15\] and \[100\].
The factors of \[15\] are \[15=1,3,5,15\]
Similarly, the factors of \[100\] are \[100=1,2,4,5,10,20,25,50,100\]
Now let us find out the common factor.
We can find that only \[5\] is the only available common factor. Since there is no other common factor, we need not compare between any.
\[\therefore \] The GCF of \[15\] and \[100\] is \[5\].

Note: GCF is also known as Highest Common Factor (HCF) or Greatest Common Divisor (GCD). The given problem can also be solved by the prime factorization method as shown below.
Firstly, let us list the prime factors of \[15\] and \[100\].
\[\begin{align}
  & 15=3\times 5 \\
 & 100=5\times 5\times 2\times 2 \\
\end{align}\]
Now from this, we have to list down the common prime factor. We can see that the common factor is \[5\].
\[\therefore \] The GCF of \[15\] and \[100\] is \[5\].