Highest Common Factor of 691, 972, 571 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 691, 972, 571 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 972, 571 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 691, 972, 571 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 691, 972, 571 is 1.

HCF(691, 972, 571) = 1

HCF of 691, 972, 571 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 691, 972, 571 is 1.

Highest Common Factor of 691,972,571 using Euclid's algorithm

Highest Common Factor of 691,972,571 is 1

Step 1: Since 972 > 691, we apply the division lemma to 972 and 691, to get

972 = 691 x 1 + 281

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 281 and 691, to get

691 = 281 x 2 + 129

Step 3: We consider the new divisor 281 and the new remainder 129, and apply the division lemma to get

281 = 129 x 2 + 23

We consider the new divisor 129 and the new remainder 23,and apply the division lemma to get

129 = 23 x 5 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 972 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(129,23) = HCF(281,129) = HCF(691,281) = HCF(972,691) .

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

Step 1: Since 571 > 1, we apply the division lemma to 571 and 1, to get

571 = 1 x 571 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 571 is 1

Notice that 1 = HCF(571,1) .

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Frequently Asked Questions on HCF of 691, 972, 571 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 691, 972, 571?

Answer: HCF of 691, 972, 571 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 972, 571 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 972, 571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.