Highest Common Factor of 837, 520, 674 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 837, 520, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 837, 520, 674 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 837, 520, 674 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 837, 520, 674 is 1.

HCF(837, 520, 674) = 1

HCF of 837, 520, 674 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 837, 520, 674 is 1.

Highest Common Factor of 837,520,674 using Euclid's algorithm

Highest Common Factor of 837,520,674 is 1

Step 1: Since 837 > 520, we apply the division lemma to 837 and 520, to get

837 = 520 x 1 + 317

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 317 and 520, to get

520 = 317 x 1 + 203

Step 3: We consider the new divisor 317 and the new remainder 203, and apply the division lemma to get

317 = 203 x 1 + 114

We consider the new divisor 203 and the new remainder 114,and apply the division lemma to get

203 = 114 x 1 + 89

We consider the new divisor 114 and the new remainder 89,and apply the division lemma to get

114 = 89 x 1 + 25

We consider the new divisor 89 and the new remainder 25,and apply the division lemma to get

89 = 25 x 3 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 837 and 520 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(89,25) = HCF(114,89) = HCF(203,114) = HCF(317,203) = HCF(520,317) = HCF(837,520) .

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

Step 1: Since 674 > 1, we apply the division lemma to 674 and 1, to get

674 = 1 x 674 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 674 is 1

Notice that 1 = HCF(674,1) .

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Frequently Asked Questions on HCF of 837, 520, 674 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 837, 520, 674?

Answer: HCF of 837, 520, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 837, 520, 674 using Euclid's Algorithm?

Answer: For arbitrary numbers 837, 520, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.