Highest Common Factor of 691, 360, 92 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, 360, 92 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 360, 92 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, 360, 92 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, 360, 92 is 1.

HCF(691, 360, 92) = 1

HCF of 691, 360, 92 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, 360, 92 is 1.

Highest Common Factor of 691,360,92 using Euclid's algorithm

Highest Common Factor of 691,360,92 is 1

Step 1: Since 691 > 360, we apply the division lemma to 691 and 360, to get

691 = 360 x 1 + 331

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 331 and 360, to get

360 = 331 x 1 + 29

Step 3: We consider the new divisor 331 and the new remainder 29, and apply the division lemma to get

331 = 29 x 11 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 691 and 360 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(331,29) = HCF(360,331) = HCF(691,360) .

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

Step 1: Since 92 > 1, we apply the division lemma to 92 and 1, to get

92 = 1 x 92 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 92 is 1

Notice that 1 = HCF(92,1) .

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Frequently Asked Questions on HCF of 691, 360, 92 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, 360, 92?

Answer: HCF of 691, 360, 92 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 360, 92 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 360, 92 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.