Highest Common Factor of 988, 9475 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, 9475 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 988, 9475 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, 9475 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, 9475 is 1.

HCF(988, 9475) = 1

HCF of 988, 9475 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, 9475 is 1.

Highest Common Factor of 988,9475 using Euclid's algorithm

Highest Common Factor of 988,9475 is 1

Step 1: Since 9475 > 988, we apply the division lemma to 9475 and 988, to get

9475 = 988 x 9 + 583

Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 583 and 988, to get

988 = 583 x 1 + 405

Step 3: We consider the new divisor 583 and the new remainder 405, and apply the division lemma to get

583 = 405 x 1 + 178

We consider the new divisor 405 and the new remainder 178,and apply the division lemma to get

405 = 178 x 2 + 49

We consider the new divisor 178 and the new remainder 49,and apply the division lemma to get

178 = 49 x 3 + 31

We consider the new divisor 49 and the new remainder 31,and apply the division lemma to get

49 = 31 x 1 + 18

We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get

31 = 18 x 1 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 988 and 9475 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(178,49) = HCF(405,178) = HCF(583,405) = HCF(988,583) = HCF(9475,988) .

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Frequently Asked Questions on HCF of 988, 9475 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, 9475?

Answer: HCF of 988, 9475 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 988, 9475 using Euclid's Algorithm?

Answer: For arbitrary numbers 988, 9475 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.