Highest Common Factor of 9998, 2667, 11617 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 9998, 2667, 11617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9998, 2667, 11617 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 9998, 2667, 11617 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 9998, 2667, 11617 is 1.

HCF(9998, 2667, 11617) = 1

HCF of 9998, 2667, 11617 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 9998, 2667, 11617 is 1.

Highest Common Factor of 9998,2667,11617 using Euclid's algorithm

Highest Common Factor of 9998,2667,11617 is 1

Step 1: Since 9998 > 2667, we apply the division lemma to 9998 and 2667, to get

9998 = 2667 x 3 + 1997

Step 2: Since the reminder 2667 ≠ 0, we apply division lemma to 1997 and 2667, to get

2667 = 1997 x 1 + 670

Step 3: We consider the new divisor 1997 and the new remainder 670, and apply the division lemma to get

1997 = 670 x 2 + 657

We consider the new divisor 670 and the new remainder 657,and apply the division lemma to get

670 = 657 x 1 + 13

We consider the new divisor 657 and the new remainder 13,and apply the division lemma to get

657 = 13 x 50 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 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 9998 and 2667 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(657,13) = HCF(670,657) = HCF(1997,670) = HCF(2667,1997) = HCF(9998,2667) .

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

Step 1: Since 11617 > 1, we apply the division lemma to 11617 and 1, to get

11617 = 1 x 11617 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11617 is 1

Notice that 1 = HCF(11617,1) .

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Frequently Asked Questions on HCF of 9998, 2667, 11617 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 9998, 2667, 11617?

Answer: HCF of 9998, 2667, 11617 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9998, 2667, 11617 using Euclid's Algorithm?

Answer: For arbitrary numbers 9998, 2667, 11617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.