Highest Common Factor of 988, 607, 514 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 988, 607, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 988, 607, 514 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 988, 607, 514 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 988, 607, 514 is 1.

HCF(988, 607, 514) = 1

HCF of 988, 607, 514 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 988, 607, 514 is 1.

Highest Common Factor of 988,607,514 using Euclid's algorithm

Highest Common Factor of 988,607,514 is 1

Step 1: Since 988 > 607, we apply the division lemma to 988 and 607, to get

988 = 607 x 1 + 381

Step 2: Since the reminder 607 ≠ 0, we apply division lemma to 381 and 607, to get

607 = 381 x 1 + 226

Step 3: We consider the new divisor 381 and the new remainder 226, and apply the division lemma to get

381 = 226 x 1 + 155

We consider the new divisor 226 and the new remainder 155,and apply the division lemma to get

226 = 155 x 1 + 71

We consider the new divisor 155 and the new remainder 71,and apply the division lemma to get

155 = 71 x 2 + 13

We consider the new divisor 71 and the new remainder 13,and apply the division lemma to get

71 = 13 x 5 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 988 and 607 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(71,13) = HCF(155,71) = HCF(226,155) = HCF(381,226) = HCF(607,381) = HCF(988,607) .

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

Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get

514 = 1 x 514 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1

Notice that 1 = HCF(514,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 988, 607, 514 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 988, 607, 514?

Answer: HCF of 988, 607, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 988, 607, 514 using Euclid's Algorithm?

Answer: For arbitrary numbers 988, 607, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.