Highest Common Factor of 180, 645, 857 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 180, 645, 857 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 645, 857 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 180, 645, 857 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 180, 645, 857 is 1.

HCF(180, 645, 857) = 1

HCF of 180, 645, 857 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 180, 645, 857 is 1.

Highest Common Factor of 180,645,857 using Euclid's algorithm

Highest Common Factor of 180,645,857 is 1

Step 1: Since 645 > 180, we apply the division lemma to 645 and 180, to get

645 = 180 x 3 + 105

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 105 and 180, to get

180 = 105 x 1 + 75

Step 3: We consider the new divisor 105 and the new remainder 75, and apply the division lemma to get

105 = 75 x 1 + 30

We consider the new divisor 75 and the new remainder 30,and apply the division lemma to get

75 = 30 x 2 + 15

We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 180 and 645 is 15

Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(105,75) = HCF(180,105) = HCF(645,180) .

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

Step 1: Since 857 > 15, we apply the division lemma to 857 and 15, to get

857 = 15 x 57 + 2

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 2 and 15, to get

15 = 2 x 7 + 1

Step 3: 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 15 and 857 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(857,15) .

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Frequently Asked Questions on HCF of 180, 645, 857 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 180, 645, 857?

Answer: HCF of 180, 645, 857 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 645, 857 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 645, 857 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.