Highest Common Factor of 694, 589, 180 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 694, 589, 180 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 694, 589, 180 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 694, 589, 180 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 694, 589, 180 is 1.

HCF(694, 589, 180) = 1

HCF of 694, 589, 180 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 694, 589, 180 is 1.

Highest Common Factor of 694,589,180 using Euclid's algorithm

Highest Common Factor of 694,589,180 is 1

Step 1: Since 694 > 589, we apply the division lemma to 694 and 589, to get

694 = 589 x 1 + 105

Step 2: Since the reminder 589 ≠ 0, we apply division lemma to 105 and 589, to get

589 = 105 x 5 + 64

Step 3: We consider the new divisor 105 and the new remainder 64, and apply the division lemma to get

105 = 64 x 1 + 41

We consider the new divisor 64 and the new remainder 41,and apply the division lemma to get

64 = 41 x 1 + 23

We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 694 and 589 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(64,41) = HCF(105,64) = HCF(589,105) = HCF(694,589) .

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

Step 1: Since 180 > 1, we apply the division lemma to 180 and 1, to get

180 = 1 x 180 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 180 is 1

Notice that 1 = HCF(180,1) .

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Frequently Asked Questions on HCF of 694, 589, 180 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 694, 589, 180?

Answer: HCF of 694, 589, 180 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 694, 589, 180 using Euclid's Algorithm?

Answer: For arbitrary numbers 694, 589, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.