Highest Common Factor of 180, 515, 138 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, 515, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 515, 138 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, 515, 138 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, 515, 138 is 1.

HCF(180, 515, 138) = 1

HCF of 180, 515, 138 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 180, 515, 138 is 1.

Highest Common Factor of 180,515,138 using Euclid's algorithm

Highest Common Factor of 180,515,138 is 1

Step 1: Since 515 > 180, we apply the division lemma to 515 and 180, to get

515 = 180 x 2 + 155

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 155 and 180, to get

180 = 155 x 1 + 25

Step 3: We consider the new divisor 155 and the new remainder 25, and apply the division lemma to get

155 = 25 x 6 + 5

We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 180 and 515 is 5

Notice that 5 = HCF(25,5) = HCF(155,25) = HCF(180,155) = HCF(515,180) .

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

Step 1: Since 138 > 5, we apply the division lemma to 138 and 5, to get

138 = 5 x 27 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 138 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(138,5) .

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Frequently Asked Questions on HCF of 180, 515, 138 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, 515, 138?

Answer: HCF of 180, 515, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 515, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 515, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.