Question

Find the HCF of 48, 72 and 84.

Answer 1

Hint:
Here we need to find the HCF of the three given numbers. HCF means the highest number that divides all three numbers. We will first find the factors of each number individually. Then we will find the highest factor which is common to all these numbers. That highest factor will be the required HCF of these three given numbers.

Complete step by step solution:
Here, we need to find the HCF of the three numbers i.e. 48, 72 and 84.
We know that the HCF of numbers means the highest number that divides all these numbers.
Now, we will first find the factors of 48.
Factors of number 48 \[ = 2 \times 2 \times 2 \times 2 \times 3\]
Now, we will first find the factors of 72.
Factors of number 72 \[ = 2 \times 2 \times 2 \times 3 \times 3\]
Now, we will first find the factors of 84.
Factors of number 84 \[ = 2 \times 2 \times 3 \times 7\]
Now, we will find the highest factor which is common to all the three numbers.
Here, we can see that the highest factor of these three numbers is \[2 \times 2 \times 3\]

Hence, the required HCF of these three numbers i.e. 48, 72 and 84 is equal to \[2 \times 2 \times 3 = 12\]

Note:
We know that the full form of HCF is the Highest Common Factor. We need to keep in mind that the Highest Common Factor of the numbers is always less than each of the numbers i.e. it cannot be greater than any of these numbers. The Highest Common Factor of the numbers is equal to the product of all the factors which are common to all the numbers.