# Highest Common Factor of 729, 864, 645 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 729, 864, 645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 729, 864, 645 is 3 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 729, 864, 645 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 729, 864, 645 is 3.

HCF(729, 864, 645) = 3

## HCF of 729, 864, 645 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 729, 864, 645 is 3. ### Highest Common Factor of 729,864,645 is 3

Step 1: Since 864 > 729, we apply the division lemma to 864 and 729, to get

864 = 729 x 1 + 135

Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 135 and 729, to get

729 = 135 x 5 + 54

Step 3: We consider the new divisor 135 and the new remainder 54, and apply the division lemma to get

135 = 54 x 2 + 27

We consider the new divisor 54 and the new remainder 27, and apply the division lemma to get

54 = 27 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 729 and 864 is 27

Notice that 27 = HCF(54,27) = HCF(135,54) = HCF(729,135) = HCF(864,729) .

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

Step 1: Since 645 > 27, we apply the division lemma to 645 and 27, to get

645 = 27 x 23 + 24

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 24 and 27, to get

27 = 24 x 1 + 3

Step 3: We consider the new divisor 24 and the new remainder 3, and apply the division lemma to get

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 645 is 3

Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(645,27) .

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### Frequently Asked Questions on HCF of 729, 864, 645 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 729, 864, 645?

Answer: HCF of 729, 864, 645 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 729, 864, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 729, 864, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.