Highest Common Factor of 9678, 7867, 16605 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 9678, 7867, 16605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9678, 7867, 16605 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 9678, 7867, 16605 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 9678, 7867, 16605 is 1.

HCF(9678, 7867, 16605) = 1

HCF of 9678, 7867, 16605 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 9678, 7867, 16605 is 1.

Highest Common Factor of 9678,7867,16605 using Euclid's algorithm

Highest Common Factor of 9678,7867,16605 is 1

Step 1: Since 9678 > 7867, we apply the division lemma to 9678 and 7867, to get

9678 = 7867 x 1 + 1811

Step 2: Since the reminder 7867 ≠ 0, we apply division lemma to 1811 and 7867, to get

7867 = 1811 x 4 + 623

Step 3: We consider the new divisor 1811 and the new remainder 623, and apply the division lemma to get

1811 = 623 x 2 + 565

We consider the new divisor 623 and the new remainder 565,and apply the division lemma to get

623 = 565 x 1 + 58

We consider the new divisor 565 and the new remainder 58,and apply the division lemma to get

565 = 58 x 9 + 43

We consider the new divisor 58 and the new remainder 43,and apply the division lemma to get

58 = 43 x 1 + 15

We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get

43 = 15 x 2 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 9678 and 7867 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(565,58) = HCF(623,565) = HCF(1811,623) = HCF(7867,1811) = HCF(9678,7867) .

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

Step 1: Since 16605 > 1, we apply the division lemma to 16605 and 1, to get

16605 = 1 x 16605 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16605 is 1

Notice that 1 = HCF(16605,1) .

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Frequently Asked Questions on HCF of 9678, 7867, 16605 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 9678, 7867, 16605?

Answer: HCF of 9678, 7867, 16605 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9678, 7867, 16605 using Euclid's Algorithm?

Answer: For arbitrary numbers 9678, 7867, 16605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.