Find the HCF of the following pair of numbers: 32 and 54

Given: 32 and 54.

To find: Here we have to find the HCF of the given numbers.

Solution:

Using Euclid's division algorithm to find HCF:

Using Euclid’s lemma to get: 

• $54\ =\ 32\ \times\ 1\ +\ 22$

Now, consider the divisor 32 and the remainder 22, and apply the division lemma to get:

• $32\ =\ 22\ \times\ 1\ +\ 10$

Now, consider the divisor 22 and the remainder 10, and apply the division lemma to get:

• $22\ =\ 10\ \times\ 2\ +\ 2$
  

Now, consider the divisor 10 and the remainder 2, and apply the division lemma to get:

• $10\ =\ 2\ \times\ 5\ +\ 0$

The remainder has become zero, and we cannot proceed any further. 

Therefore the HCF of 54 and 32 is the divisor at this stage, i.e., 2.

So, HCF of 32 and 54 is 2.

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Updated on: 10-Oct-2022

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