Highest Common Factor of 691, 180, 405 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, 180, 405 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 180, 405 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, 180, 405 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, 180, 405 is 1.

HCF(691, 180, 405) = 1

HCF of 691, 180, 405 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, 180, 405 is 1.

Highest Common Factor of 691,180,405 using Euclid's algorithm

Highest Common Factor of 691,180,405 is 1

Step 1: Since 691 > 180, we apply the division lemma to 691 and 180, to get

691 = 180 x 3 + 151

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 151 and 180, to get

180 = 151 x 1 + 29

Step 3: We consider the new divisor 151 and the new remainder 29, and apply the division lemma to get

151 = 29 x 5 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 180 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(151,29) = HCF(180,151) = HCF(691,180) .

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

Step 1: Since 405 > 1, we apply the division lemma to 405 and 1, to get

405 = 1 x 405 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 405 is 1

Notice that 1 = HCF(405,1) .

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Frequently Asked Questions on HCF of 691, 180, 405 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, 180, 405?

Answer: HCF of 691, 180, 405 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 180, 405 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 180, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.