Highest Common Factor of 685, 1166 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 685, 1166 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 1166 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 685, 1166 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 685, 1166 is 1.

HCF(685, 1166) = 1

HCF of 685, 1166 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 685, 1166 is 1.

Highest Common Factor of 685,1166 using Euclid's algorithm

Highest Common Factor of 685,1166 is 1

Step 1: Since 1166 > 685, we apply the division lemma to 1166 and 685, to get

1166 = 685 x 1 + 481

Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 481 and 685, to get

685 = 481 x 1 + 204

Step 3: We consider the new divisor 481 and the new remainder 204, and apply the division lemma to get

481 = 204 x 2 + 73

We consider the new divisor 204 and the new remainder 73,and apply the division lemma to get

204 = 73 x 2 + 58

We consider the new divisor 73 and the new remainder 58,and apply the division lemma to get

73 = 58 x 1 + 15

We consider the new divisor 58 and the new remainder 15,and apply the division lemma to get

58 = 15 x 3 + 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 685 and 1166 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(58,15) = HCF(73,58) = HCF(204,73) = HCF(481,204) = HCF(685,481) = HCF(1166,685) .

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Frequently Asked Questions on HCF of 685, 1166 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 685, 1166?

Answer: HCF of 685, 1166 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 1166 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 1166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.