Highest Common Factor of 572, 8609, 6725 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 572, 8609, 6725 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 572, 8609, 6725 is 1 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 572, 8609, 6725 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 572, 8609, 6725 is 1.

HCF(572, 8609, 6725) = 1

HCF of 572, 8609, 6725 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 572, 8609, 6725 is 1.

Highest Common Factor of 572,8609,6725 using Euclid's algorithm

Highest Common Factor of 572,8609,6725 is 1

Step 1: Since 8609 > 572, we apply the division lemma to 8609 and 572, to get

8609 = 572 x 15 + 29

Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 29 and 572, to get

572 = 29 x 19 + 21

Step 3: We consider the new divisor 29 and the new remainder 21, and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 572 and 8609 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(572,29) = HCF(8609,572) .

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

Step 1: Since 6725 > 1, we apply the division lemma to 6725 and 1, to get

6725 = 1 x 6725 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6725 is 1

Notice that 1 = HCF(6725,1) .

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Frequently Asked Questions on HCF of 572, 8609, 6725 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 572, 8609, 6725?

Answer: HCF of 572, 8609, 6725 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 572, 8609, 6725 using Euclid's Algorithm?

Answer: For arbitrary numbers 572, 8609, 6725 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.