Highest Common Factor of 583, 988, 746 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 583, 988, 746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 583, 988, 746 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 583, 988, 746 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 583, 988, 746 is 1.

HCF(583, 988, 746) = 1

HCF of 583, 988, 746 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 583, 988, 746 is 1.

Highest Common Factor of 583,988,746 using Euclid's algorithm

Highest Common Factor of 583,988,746 is 1

Step 1: Since 988 > 583, we apply the division lemma to 988 and 583, to get

988 = 583 x 1 + 405

Step 2: Since the reminder 583 ≠ 0, we apply division lemma to 405 and 583, to get

583 = 405 x 1 + 178

Step 3: We consider the new divisor 405 and the new remainder 178, and apply the division lemma to get

405 = 178 x 2 + 49

We consider the new divisor 178 and the new remainder 49,and apply the division lemma to get

178 = 49 x 3 + 31

We consider the new divisor 49 and the new remainder 31,and apply the division lemma to get

49 = 31 x 1 + 18

We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get

31 = 18 x 1 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 583 and 988 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(178,49) = HCF(405,178) = HCF(583,405) = HCF(988,583) .

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

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

746 = 1 x 746 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 746 is 1

Notice that 1 = HCF(746,1) .

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Frequently Asked Questions on HCF of 583, 988, 746 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 583, 988, 746?

Answer: HCF of 583, 988, 746 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 583, 988, 746 using Euclid's Algorithm?

Answer: For arbitrary numbers 583, 988, 746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.