Highest Common Factor of 9666, 2286 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 9666, 2286 i.e. 18 the largest integer that leaves a remainder zero for all numbers.

HCF of 9666, 2286 is 18 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 9666, 2286 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 9666, 2286 is 18.

HCF(9666, 2286) = 18

HCF of 9666, 2286 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 9666, 2286 is 18.

Highest Common Factor of 9666,2286 using Euclid's algorithm

Highest Common Factor of 9666,2286 is 18

Step 1: Since 9666 > 2286, we apply the division lemma to 9666 and 2286, to get

9666 = 2286 x 4 + 522

Step 2: Since the reminder 2286 ≠ 0, we apply division lemma to 522 and 2286, to get

2286 = 522 x 4 + 198

Step 3: We consider the new divisor 522 and the new remainder 198, and apply the division lemma to get

522 = 198 x 2 + 126

We consider the new divisor 198 and the new remainder 126,and apply the division lemma to get

198 = 126 x 1 + 72

We consider the new divisor 126 and the new remainder 72,and apply the division lemma to get

126 = 72 x 1 + 54

We consider the new divisor 72 and the new remainder 54,and apply the division lemma to get

72 = 54 x 1 + 18

We consider the new divisor 54 and the new remainder 18,and apply the division lemma to get

54 = 18 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 9666 and 2286 is 18

Notice that 18 = HCF(54,18) = HCF(72,54) = HCF(126,72) = HCF(198,126) = HCF(522,198) = HCF(2286,522) = HCF(9666,2286) .

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Frequently Asked Questions on HCF of 9666, 2286 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 9666, 2286?

Answer: HCF of 9666, 2286 is 18 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9666, 2286 using Euclid's Algorithm?

Answer: For arbitrary numbers 9666, 2286 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.