Highest Common Factor of 585, 386, 780, 205 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 585, 386, 780, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 386, 780, 205 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 585, 386, 780, 205 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 585, 386, 780, 205 is 1.

HCF(585, 386, 780, 205) = 1

HCF of 585, 386, 780, 205 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 585, 386, 780, 205 is 1.

Highest Common Factor of 585,386,780,205 using Euclid's algorithm

Highest Common Factor of 585,386,780,205 is 1

Step 1: Since 585 > 386, we apply the division lemma to 585 and 386, to get

585 = 386 x 1 + 199

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 199 and 386, to get

386 = 199 x 1 + 187

Step 3: We consider the new divisor 199 and the new remainder 187, and apply the division lemma to get

199 = 187 x 1 + 12

We consider the new divisor 187 and the new remainder 12,and apply the division lemma to get

187 = 12 x 15 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 585 and 386 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(187,12) = HCF(199,187) = HCF(386,199) = HCF(585,386) .

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

Step 1: Since 780 > 1, we apply the division lemma to 780 and 1, to get

780 = 1 x 780 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 780 is 1

Notice that 1 = HCF(780,1) .

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

Step 1: Since 205 > 1, we apply the division lemma to 205 and 1, to get

205 = 1 x 205 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 205 is 1

Notice that 1 = HCF(205,1) .

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Frequently Asked Questions on HCF of 585, 386, 780, 205 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 585, 386, 780, 205?

Answer: HCF of 585, 386, 780, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 386, 780, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 386, 780, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.