Highest Common Factor of 609, 686 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 609, 686 i.e. 7 the largest integer that leaves a remainder zero for all numbers.

HCF of 609, 686 is 7 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 609, 686 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 609, 686 is 7.

HCF(609, 686) = 7

HCF of 609, 686 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 609, 686 is 7.

Highest Common Factor of 609,686 using Euclid's algorithm

Highest Common Factor of 609,686 is 7

Step 1: Since 686 > 609, we apply the division lemma to 686 and 609, to get

686 = 609 x 1 + 77

Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 77 and 609, to get

609 = 77 x 7 + 70

Step 3: We consider the new divisor 77 and the new remainder 70, and apply the division lemma to get

77 = 70 x 1 + 7

We consider the new divisor 70 and the new remainder 7, and apply the division lemma to get

70 = 7 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 609 and 686 is 7

Notice that 7 = HCF(70,7) = HCF(77,70) = HCF(609,77) = HCF(686,609) .

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Frequently Asked Questions on HCF of 609, 686 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 609, 686?

Answer: HCF of 609, 686 is 7 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 609, 686 using Euclid's Algorithm?

Answer: For arbitrary numbers 609, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.