# Highest Common Factor of 27, 45, 108, 126 using Euclid's algorithm

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 27, 45, 108, 126 i.e. 9 the largest integer that leaves a remainder zero for all numbers.

HCF of 27, 45, 108, 126 is 9 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 27, 45, 108, 126 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 27, 45, 108, 126 is 9.

HCF(27, 45, 108, 126) = 9

## HCF of 27, 45, 108, 126 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 27, 45, 108, 126 is 9.

### Highest Common Factor of 27,45,108,126 using Euclid's algorithm

Step 1: Since 45 > 27, we apply the division lemma to 45 and 27, to get

45 = 27 x 1 + 18

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 18 and 27, to get

27 = 18 x 1 + 9

Step 3: We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 27 and 45 is 9

Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 108 > 9, we apply the division lemma to 108 and 9, to get

108 = 9 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 108 is 9

Notice that 9 = HCF(108,9) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 126 > 9, we apply the division lemma to 126 and 9, to get

126 = 9 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 126 is 9

Notice that 9 = HCF(126,9) .

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### Frequently Asked Questions on HCF of 27, 45, 108, 126 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 27, 45, 108, 126?

Answer: HCF of 27, 45, 108, 126 is 9 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 27, 45, 108, 126 using Euclid's Algorithm?

Answer: For arbitrary numbers 27, 45, 108, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.