Highest Common Factor of 612, 406, 329 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, 406, 329 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 406, 329 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, 406, 329 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, 406, 329 is 1.

HCF(612, 406, 329) = 1

HCF of 612, 406, 329 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 612, 406, 329 is 1.

Highest Common Factor of 612,406,329 using Euclid's algorithm

Highest Common Factor of 612,406,329 is 1

Step 1: Since 612 > 406, we apply the division lemma to 612 and 406, to get

612 = 406 x 1 + 206

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 206 and 406, to get

406 = 206 x 1 + 200

Step 3: We consider the new divisor 206 and the new remainder 200, and apply the division lemma to get

206 = 200 x 1 + 6

We consider the new divisor 200 and the new remainder 6,and apply the division lemma to get

200 = 6 x 33 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 612 and 406 is 2

Notice that 2 = HCF(6,2) = HCF(200,6) = HCF(206,200) = HCF(406,206) = HCF(612,406) .

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

Step 1: Since 329 > 2, we apply the division lemma to 329 and 2, to get

329 = 2 x 164 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 329 is 1

Notice that 1 = HCF(2,1) = HCF(329,2) .

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Frequently Asked Questions on HCF of 612, 406, 329 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, 406, 329?

Answer: HCF of 612, 406, 329 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 406, 329 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 406, 329 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.