Highest Common Factor of 9667, 6662 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 9667, 6662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9667, 6662 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 9667, 6662 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 9667, 6662 is 1.

HCF(9667, 6662) = 1

HCF of 9667, 6662 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 9667, 6662 is 1.

Highest Common Factor of 9667,6662 using Euclid's algorithm

Highest Common Factor of 9667,6662 is 1

Step 1: Since 9667 > 6662, we apply the division lemma to 9667 and 6662, to get

9667 = 6662 x 1 + 3005

Step 2: Since the reminder 6662 ≠ 0, we apply division lemma to 3005 and 6662, to get

6662 = 3005 x 2 + 652

Step 3: We consider the new divisor 3005 and the new remainder 652, and apply the division lemma to get

3005 = 652 x 4 + 397

We consider the new divisor 652 and the new remainder 397,and apply the division lemma to get

652 = 397 x 1 + 255

We consider the new divisor 397 and the new remainder 255,and apply the division lemma to get

397 = 255 x 1 + 142

We consider the new divisor 255 and the new remainder 142,and apply the division lemma to get

255 = 142 x 1 + 113

We consider the new divisor 142 and the new remainder 113,and apply the division lemma to get

142 = 113 x 1 + 29

We consider the new divisor 113 and the new remainder 29,and apply the division lemma to get

113 = 29 x 3 + 26

We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get

29 = 26 x 1 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 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 9667 and 6662 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(113,29) = HCF(142,113) = HCF(255,142) = HCF(397,255) = HCF(652,397) = HCF(3005,652) = HCF(6662,3005) = HCF(9667,6662) .

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Frequently Asked Questions on HCF of 9667, 6662 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 9667, 6662?

Answer: HCF of 9667, 6662 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9667, 6662 using Euclid's Algorithm?

Answer: For arbitrary numbers 9667, 6662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.