Highest Common Factor of 586, 844, 998 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 586, 844, 998 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 844, 998 is 2 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 586, 844, 998 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 586, 844, 998 is 2.

HCF(586, 844, 998) = 2

HCF of 586, 844, 998 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 586, 844, 998 is 2.

Highest Common Factor of 586,844,998 using Euclid's algorithm

Highest Common Factor of 586,844,998 is 2

Step 1: Since 844 > 586, we apply the division lemma to 844 and 586, to get

844 = 586 x 1 + 258

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 258 and 586, to get

586 = 258 x 2 + 70

Step 3: We consider the new divisor 258 and the new remainder 70, and apply the division lemma to get

258 = 70 x 3 + 48

We consider the new divisor 70 and the new remainder 48,and apply the division lemma to get

70 = 48 x 1 + 22

We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get

48 = 22 x 2 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 586 and 844 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(70,48) = HCF(258,70) = HCF(586,258) = HCF(844,586) .

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

Step 1: Since 998 > 2, we apply the division lemma to 998 and 2, to get

998 = 2 x 499 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 998 is 2

Notice that 2 = HCF(998,2) .

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Frequently Asked Questions on HCF of 586, 844, 998 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 586, 844, 998?

Answer: HCF of 586, 844, 998 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 844, 998 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 844, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.