Highest Common Factor of 612, 746, 683 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 612, 746, 683 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 746, 683 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 612, 746, 683 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 612, 746, 683 is 1.

HCF(612, 746, 683) = 1

HCF of 612, 746, 683 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 612, 746, 683 is 1.

Highest Common Factor of 612,746,683 using Euclid's algorithm

Highest Common Factor of 612,746,683 is 1

Step 1: Since 746 > 612, we apply the division lemma to 746 and 612, to get

746 = 612 x 1 + 134

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 134 and 612, to get

612 = 134 x 4 + 76

Step 3: We consider the new divisor 134 and the new remainder 76, and apply the division lemma to get

134 = 76 x 1 + 58

We consider the new divisor 76 and the new remainder 58,and apply the division lemma to get

76 = 58 x 1 + 18

We consider the new divisor 58 and the new remainder 18,and apply the division lemma to get

58 = 18 x 3 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 612 and 746 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(58,18) = HCF(76,58) = HCF(134,76) = HCF(612,134) = HCF(746,612) .

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

Step 1: Since 683 > 2, we apply the division lemma to 683 and 2, to get

683 = 2 x 341 + 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 683 is 1

Notice that 1 = HCF(2,1) = HCF(683,2) .

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Frequently Asked Questions on HCF of 612, 746, 683 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 612, 746, 683?

Answer: HCF of 612, 746, 683 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 746, 683 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 746, 683 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.