Highest Common Factor of 204, 691, 677 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 204, 691, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 204, 691, 677 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 204, 691, 677 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 204, 691, 677 is 1.

HCF(204, 691, 677) = 1

HCF of 204, 691, 677 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 204, 691, 677 is 1.

Highest Common Factor of 204,691,677 using Euclid's algorithm

Highest Common Factor of 204,691,677 is 1

Step 1: Since 691 > 204, we apply the division lemma to 691 and 204, to get

691 = 204 x 3 + 79

Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 79 and 204, to get

204 = 79 x 2 + 46

Step 3: We consider the new divisor 79 and the new remainder 46, and apply the division lemma to get

79 = 46 x 1 + 33

We consider the new divisor 46 and the new remainder 33,and apply the division lemma to get

46 = 33 x 1 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 204 and 691 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(46,33) = HCF(79,46) = HCF(204,79) = HCF(691,204) .

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

Step 1: Since 677 > 1, we apply the division lemma to 677 and 1, to get

677 = 1 x 677 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 677 is 1

Notice that 1 = HCF(677,1) .

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Frequently Asked Questions on HCF of 204, 691, 677 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 204, 691, 677?

Answer: HCF of 204, 691, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 204, 691, 677 using Euclid's Algorithm?

Answer: For arbitrary numbers 204, 691, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.