Question

Find the H.C.F of 2, 3 and 5.

Answer 1

Hint: First of all, we should write all factors 2, 3 and 5. Now we should consider the common factors of 2, 3 and 5. Among the factors of 2, 3 and 5, we have to find the highest common factor of 2, 3 and 5. The highest common factor of 2, 3 and 5 gives the H.C.F of 2, 3 and 5. In this way, we can find the H.C.F of 2, 3 and 5.

Complete step-by-step answer:
Before solving the question, we should understand the concept of H.C.F. To find H.C.F of three numbers, we should mention each and every factor of three numbers. Now we have to write all the common factors of three numbers. Among the common factors, we have to find the highest common factor. This highest common factor is called H.C.F.
In the question, we are given three numbers 2,3 and 5. Now we have to find the H.C.F of 2,3,5.
\[\begin{align}
  & 2=2\times 1....(1) \\
 & 3=3\times 1....(2) \\
 & 5=5\times 1....(3) \\
\end{align}\]
From equation (1), equation (2) and equation (3), we are having the factors of 2, 3 and 5.
The common factor of 2, 3 and 5 is 1.
So, the H.C.F of 2, 3 and 5 is equal to 1.

Note: This problem can be solved in an alternative method also.
We know that the product of n numbers is equal to H.C.F of n numbers and L.C.M of n numbers.
From the question, we are given to find the H.C.F of 2,3 and 5.
The product of 2,3 and 5 \[=2\times 3\times 5=30\]
Now have to find the L.C.M of 2,3 and 5.
The multiples of 2 are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36, …
The multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36, 39, ……
The multiples of 5 are 5,10,15,20,25,30,35,40,45, 50, …….
The common multiples of 2,3 and 5 are 30, 60, 90, ….
The least common multiple of 2,3 and 5 is 30.
So, the L.C.M of 2,3 and 5 is equal to 30.
We know that the product of 2,3 and 5 is equal to H.C.F of 2,3 and 5 and L.C.M of 2,3 and 5.
\[\begin{align}
  & \Rightarrow 30=30\times \text{H}\text{.C}\text{.F} \\
 & \Rightarrow \text{H}\text{.C}\text{.F=1} \\
\end{align}\]
So, the H.C.F of 2, 3 and 5 is equal 1.