Highest Common Factor of 685, 121, 194 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, 121, 194 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 121, 194 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, 121, 194 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, 121, 194 is 1.

HCF(685, 121, 194) = 1

HCF of 685, 121, 194 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, 121, 194 is 1.

Highest Common Factor of 685,121,194 using Euclid's algorithm

Highest Common Factor of 685,121,194 is 1

Step 1: Since 685 > 121, we apply the division lemma to 685 and 121, to get

685 = 121 x 5 + 80

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 80 and 121, to get

121 = 80 x 1 + 41

Step 3: We consider the new divisor 80 and the new remainder 41, and apply the division lemma to get

80 = 41 x 1 + 39

We consider the new divisor 41 and the new remainder 39,and apply the division lemma to get

41 = 39 x 1 + 2

We consider the new divisor 39 and the new remainder 2,and apply the division lemma to get

39 = 2 x 19 + 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 121 is 1

Notice that 1 = HCF(2,1) = HCF(39,2) = HCF(41,39) = HCF(80,41) = HCF(121,80) = HCF(685,121) .

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

Step 1: Since 194 > 1, we apply the division lemma to 194 and 1, to get

194 = 1 x 194 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 194 is 1

Notice that 1 = HCF(194,1) .

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Frequently Asked Questions on HCF of 685, 121, 194 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, 121, 194?

Answer: HCF of 685, 121, 194 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 121, 194 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 121, 194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.