Highest Common Factor of 8998, 7316, 57077 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 8998, 7316, 57077 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8998, 7316, 57077 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 8998, 7316, 57077 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 8998, 7316, 57077 is 1.

HCF(8998, 7316, 57077) = 1

HCF of 8998, 7316, 57077 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 8998, 7316, 57077 is 1.

Highest Common Factor of 8998,7316,57077 using Euclid's algorithm

Highest Common Factor of 8998,7316,57077 is 1

Step 1: Since 8998 > 7316, we apply the division lemma to 8998 and 7316, to get

8998 = 7316 x 1 + 1682

Step 2: Since the reminder 7316 ≠ 0, we apply division lemma to 1682 and 7316, to get

7316 = 1682 x 4 + 588

Step 3: We consider the new divisor 1682 and the new remainder 588, and apply the division lemma to get

1682 = 588 x 2 + 506

We consider the new divisor 588 and the new remainder 506,and apply the division lemma to get

588 = 506 x 1 + 82

We consider the new divisor 506 and the new remainder 82,and apply the division lemma to get

506 = 82 x 6 + 14

We consider the new divisor 82 and the new remainder 14,and apply the division lemma to get

82 = 14 x 5 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8998 and 7316 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(82,14) = HCF(506,82) = HCF(588,506) = HCF(1682,588) = HCF(7316,1682) = HCF(8998,7316) .

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

Step 1: Since 57077 > 2, we apply the division lemma to 57077 and 2, to get

57077 = 2 x 28538 + 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 57077 is 1

Notice that 1 = HCF(2,1) = HCF(57077,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8998, 7316, 57077 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 8998, 7316, 57077?

Answer: HCF of 8998, 7316, 57077 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8998, 7316, 57077 using Euclid's Algorithm?

Answer: For arbitrary numbers 8998, 7316, 57077 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.