Highest Common Factor of 689, 506, 837 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 689, 506, 837 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 506, 837 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 689, 506, 837 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 689, 506, 837 is 1.

HCF(689, 506, 837) = 1

HCF of 689, 506, 837 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 689, 506, 837 is 1.

Highest Common Factor of 689,506,837 using Euclid's algorithm

Highest Common Factor of 689,506,837 is 1

Step 1: Since 689 > 506, we apply the division lemma to 689 and 506, to get

689 = 506 x 1 + 183

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 183 and 506, to get

506 = 183 x 2 + 140

Step 3: We consider the new divisor 183 and the new remainder 140, and apply the division lemma to get

183 = 140 x 1 + 43

We consider the new divisor 140 and the new remainder 43,and apply the division lemma to get

140 = 43 x 3 + 11

We consider the new divisor 43 and the new remainder 11,and apply the division lemma to get

43 = 11 x 3 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 506 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(43,11) = HCF(140,43) = HCF(183,140) = HCF(506,183) = HCF(689,506) .

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

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

837 = 1 x 837 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 837 is 1

Notice that 1 = HCF(837,1) .

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Frequently Asked Questions on HCF of 689, 506, 837 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 689, 506, 837?

Answer: HCF of 689, 506, 837 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 506, 837 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 506, 837 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.