Question

HCF of 960 and 432 is ………..

Answer 1

Hint: Here we will first find the factors of the given two numbers. We will find the factors which are common in both the factorization of the numbers. Then we will multiply all these factors and the resultant numbers will be the required HCF of these two numbers.

Complete step by step solution:
Here we need to find the HCF of the given two numbers and the given two numbers are 960 and 432.
So we will first find the factors of the given two numbers.
Now, we will find the factors of the first number i.e. 960.
\[960 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5\]
Similarly, we will find the factors of the second number i.e. 432.
\[432 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3\]
Now, we will find the factors which are common in both the numbers.
We can see that the factors \[2 \times 2 \times 2 \times 2 \times 3\] are common factors of both the numbers.
So we will find the product of the numbers to find the HCF of the given two numbers i.e. 960 and 432.
HCF of 960 and 432 \[ = 2 \times 2 \times 2 \times 2 \times 3 = 48\]

Therefore, the HCF of 960 and 432 is equal to 48.

Note:
Here we obtained the value of the HCF or the Highest common factor of the given two numbers. We know that the HCF of the two numbers is defined as the largest number which completely divides both the numbers. We need to keep in mind that to proceed with the problem of HCF, we need to first find the factors of the two numbers. We should not get confused between LCM and HCF of a number. LCM of two or more numbers is a number which is evenly divisible by the given numbers. The product of two numbers is equal to the product of their LCM and HCF.