Question

What is the HCF of \[45,30,15\]?

Answer 1

Hint: From the given question we are asked to find the HCF of three numbers. To solve the problem, we should know the basic concepts of the highest common factor simply termed as HCF. Basically, we will try to find the number of divisors for the given numbers and then among the divisors we will find the largest divisor to find the highest common factor. So, our solution will be as follows.

Complete step-by-step answer:
Generally the HCF defines the greatest factor present among the given two or more numbers.
We will find the prime factorisation of the given set of numbers and then we will find the common factors which are present in all the given numbers.
For those all common factors we will use the basic operation in mathematics which is multiplication and get the required solution.
So, the prime factorisation for the given set of numbers in our question will be as follows.
\[\begin{align}
  & \Rightarrow 45=3\times 3\times 5 \\
 & \Rightarrow 30=2\times 3\times 5 \\
 & \Rightarrow 15=3\times 5 \\
\end{align}\]
So, from the above prime factorisation we can say that the common factors are \[3,5\]
Therefore, the HCF will be a product of these two numbers which is as follows.
\[\Rightarrow 3\times 5=15\]

Note: Students must have good knowledge in the concept of prime factorisation. After finding all the common factors we should not write the answer as the highest factor among the all common factors because the answer will be the product of all the common factors.
Here the number \[5\] is not the HCF as it is highest among all common factors because the answer will be product. Therefore the answer will be \[\Rightarrow 3\times 5=15\].