Highest Common Factor of 983, 638, 585 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 983, 638, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 983, 638, 585 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 983, 638, 585 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 983, 638, 585 is 1.

HCF(983, 638, 585) = 1

HCF of 983, 638, 585 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 983, 638, 585 is 1.

Highest Common Factor of 983,638,585 using Euclid's algorithm

Highest Common Factor of 983,638,585 is 1

Step 1: Since 983 > 638, we apply the division lemma to 983 and 638, to get

983 = 638 x 1 + 345

Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 345 and 638, to get

638 = 345 x 1 + 293

Step 3: We consider the new divisor 345 and the new remainder 293, and apply the division lemma to get

345 = 293 x 1 + 52

We consider the new divisor 293 and the new remainder 52,and apply the division lemma to get

293 = 52 x 5 + 33

We consider the new divisor 52 and the new remainder 33,and apply the division lemma to get

52 = 33 x 1 + 19

We consider the new divisor 33 and the new remainder 19,and apply the division lemma to get

33 = 19 x 1 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 983 and 638 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(52,33) = HCF(293,52) = HCF(345,293) = HCF(638,345) = HCF(983,638) .

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

Step 1: Since 585 > 1, we apply the division lemma to 585 and 1, to get

585 = 1 x 585 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 585 is 1

Notice that 1 = HCF(585,1) .

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Frequently Asked Questions on HCF of 983, 638, 585 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 983, 638, 585?

Answer: HCF of 983, 638, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 983, 638, 585 using Euclid's Algorithm?

Answer: For arbitrary numbers 983, 638, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.