Highest Common Factor of 572, 8371, 5198 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 572, 8371, 5198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 572, 8371, 5198 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 572, 8371, 5198 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 572, 8371, 5198 is 1.

HCF(572, 8371, 5198) = 1

HCF of 572, 8371, 5198 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 572, 8371, 5198 is 1.

Highest Common Factor of 572,8371,5198 using Euclid's algorithm

Highest Common Factor of 572,8371,5198 is 1

Step 1: Since 8371 > 572, we apply the division lemma to 8371 and 572, to get

8371 = 572 x 14 + 363

Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 363 and 572, to get

572 = 363 x 1 + 209

Step 3: We consider the new divisor 363 and the new remainder 209, and apply the division lemma to get

363 = 209 x 1 + 154

We consider the new divisor 209 and the new remainder 154,and apply the division lemma to get

209 = 154 x 1 + 55

We consider the new divisor 154 and the new remainder 55,and apply the division lemma to get

154 = 55 x 2 + 44

We consider the new divisor 55 and the new remainder 44,and apply the division lemma to get

55 = 44 x 1 + 11

We consider the new divisor 44 and the new remainder 11,and apply the division lemma to get

44 = 11 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 572 and 8371 is 11

Notice that 11 = HCF(44,11) = HCF(55,44) = HCF(154,55) = HCF(209,154) = HCF(363,209) = HCF(572,363) = HCF(8371,572) .

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

Step 1: Since 5198 > 11, we apply the division lemma to 5198 and 11, to get

5198 = 11 x 472 + 6

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 6 and 11, to get

11 = 6 x 1 + 5

Step 3: We consider the new divisor 6 and the new remainder 5, and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 5198 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(5198,11) .

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Frequently Asked Questions on HCF of 572, 8371, 5198 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 572, 8371, 5198?

Answer: HCF of 572, 8371, 5198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 572, 8371, 5198 using Euclid's Algorithm?

Answer: For arbitrary numbers 572, 8371, 5198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.