The HCF of 45 108 and 27 and 54 is 9. HCF refers to the highest common divisor that can divide all given numbers completely without any reminder.

Now! we will see the HCF of 45 108 and 27 [ 45 108 27 and 54] by different methods.

## HCF of 45 108 and 27

Find the HCF of 45 108 and 27 54 by the following methods:

- Prime factorization method.
- Listing Common Factors.
- Long Division Method.

### Find the HCF of 45 108 and 27 54 by Prime Factorization Method

For finding the HCF of 45 108 and 27 54 by Prime Factorization Method. We will do the factors of these given numbers.

Factors of 45

45 = 3X3X5

Factors of 108

108 = 2X2X3X3X3

Factors of 27

27 = 3X3X3

Factors of 54

54 = 3X3X3X2

45 = 3X3X5

108 = 3X3X3X2X2

27 = 3X3X3

54 = 3X3X3X2

Here we can see that only 3X3 are the highest common factors.

Hence The HCF of 45 108 and 27 is 9.

Similarly, the HCF of 45, 108, 27, 54 is 9.

### HCF of 45 108 and 27 by Listing Common Factors

For finding the HCF of 45, 108, 27, 54 by listing common factors we have to do the factors. As we already have factors then write them below including 1.

45 = 1X3X5X9X15X45

108 = 1X2X3X4X6X9X12X27X54X108

27 = 1X3X9X27

54 = 1X2X3X6X9X18X54

So, here we can see all these numbers can be divided by the 9 highest factors.

Therefore, The HCF of 45, 108, 27, 54 is 9.

### HCF of 45 108 and 27 54 by Long Division Method

In the long division method, we will take the two smallest numbers out of the given numbers.

In our question, we have 45, 108, 27, and 54 numbers.

So, we will take 27 and 45 as these are the smallest numbers.

Now we will divide the highest number with the smallest number. (As we take 27 and 54, we will divide 45 by 27.)

This process will be repeated again and again until we will get the 0 reminders. Check the below reference solution.

- Here when we divide 45 by 27 we get 18 reminder.
- Again we divide 27 by the reminder and we got 9 as reminder.
- Again we divide 18 by the reminder 9 and it divides the number 18 completely.
- Hence our last divisior is 9.

The HCF of 27 and 45 is 9. Hence the HCF of 45, 108, 27 and 54 is 9.

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