Highest Common Factor of 682, 480, 657, 584 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 682, 480, 657, 584 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 682, 480, 657, 584 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 682, 480, 657, 584 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 682, 480, 657, 584 is 1.

HCF(682, 480, 657, 584) = 1

HCF of 682, 480, 657, 584 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 682, 480, 657, 584 is 1.

Highest Common Factor of 682,480,657,584 using Euclid's algorithm

Highest Common Factor of 682,480,657,584 is 1

Step 1: Since 682 > 480, we apply the division lemma to 682 and 480, to get

682 = 480 x 1 + 202

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 202 and 480, to get

480 = 202 x 2 + 76

Step 3: We consider the new divisor 202 and the new remainder 76, and apply the division lemma to get

202 = 76 x 2 + 50

We consider the new divisor 76 and the new remainder 50,and apply the division lemma to get

76 = 50 x 1 + 26

We consider the new divisor 50 and the new remainder 26,and apply the division lemma to get

50 = 26 x 1 + 24

We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get

26 = 24 x 1 + 2

We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 682 and 480 is 2

Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(50,26) = HCF(76,50) = HCF(202,76) = HCF(480,202) = HCF(682,480) .

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

Step 1: Since 657 > 2, we apply the division lemma to 657 and 2, to get

657 = 2 x 328 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 657 is 1

Notice that 1 = HCF(2,1) = HCF(657,2) .

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

Step 1: Since 584 > 1, we apply the division lemma to 584 and 1, to get

584 = 1 x 584 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 584 is 1

Notice that 1 = HCF(584,1) .

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Frequently Asked Questions on HCF of 682, 480, 657, 584 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 682, 480, 657, 584?

Answer: HCF of 682, 480, 657, 584 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 682, 480, 657, 584 using Euclid's Algorithm?

Answer: For arbitrary numbers 682, 480, 657, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.