Highest Common Factor of 685, 954 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, 954 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 954 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, 954 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, 954 is 1.

HCF(685, 954) = 1

HCF of 685, 954 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, 954 is 1.

Highest Common Factor of 685,954 using Euclid's algorithm

Highest Common Factor of 685,954 is 1

Step 1: Since 954 > 685, we apply the division lemma to 954 and 685, to get

954 = 685 x 1 + 269

Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 269 and 685, to get

685 = 269 x 2 + 147

Step 3: We consider the new divisor 269 and the new remainder 147, and apply the division lemma to get

269 = 147 x 1 + 122

We consider the new divisor 147 and the new remainder 122,and apply the division lemma to get

147 = 122 x 1 + 25

We consider the new divisor 122 and the new remainder 25,and apply the division lemma to get

122 = 25 x 4 + 22

We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get

25 = 22 x 1 + 3

We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get

22 = 3 x 7 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 685 and 954 is 1

Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(122,25) = HCF(147,122) = HCF(269,147) = HCF(685,269) = HCF(954,685) .

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Frequently Asked Questions on HCF of 685, 954 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, 954?

Answer: HCF of 685, 954 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 954 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.