Highest Common Factor of 680, 612 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 680, 612 i.e. 68 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 612 is 68 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 680, 612 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 680, 612 is 68.

HCF(680, 612) = 68

HCF of 680, 612 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 680, 612 is 68.

Highest Common Factor of 680,612 using Euclid's algorithm

Highest Common Factor of 680,612 is 68

Step 1: Since 680 > 612, we apply the division lemma to 680 and 612, to get

680 = 612 x 1 + 68

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 68 and 612, to get

612 = 68 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 68, the HCF of 680 and 612 is 68

Notice that 68 = HCF(612,68) = HCF(680,612) .

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Frequently Asked Questions on HCF of 680, 612 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 680, 612?

Answer: HCF of 680, 612 is 68 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 612 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.