Highest Common Factor of 612, 216, 635 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 612, 216, 635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 216, 635 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 612, 216, 635 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 612, 216, 635 is 1.

HCF(612, 216, 635) = 1

HCF of 612, 216, 635 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 612, 216, 635 is 1.

Highest Common Factor of 612,216,635 using Euclid's algorithm

Highest Common Factor of 612,216,635 is 1

Step 1: Since 612 > 216, we apply the division lemma to 612 and 216, to get

612 = 216 x 2 + 180

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 180 and 216, to get

216 = 180 x 1 + 36

Step 3: We consider the new divisor 180 and the new remainder 36, and apply the division lemma to get

180 = 36 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 612 and 216 is 36

Notice that 36 = HCF(180,36) = HCF(216,180) = HCF(612,216) .

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

Step 1: Since 635 > 36, we apply the division lemma to 635 and 36, to get

635 = 36 x 17 + 23

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 23 and 36, to get

36 = 23 x 1 + 13

Step 3: We consider the new divisor 23 and the new remainder 13, and apply the division lemma to get

23 = 13 x 1 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 36 and 635 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(635,36) .

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Frequently Asked Questions on HCF of 612, 216, 635 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 612, 216, 635?

Answer: HCF of 612, 216, 635 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 216, 635 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 216, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.