Highest Common Factor of 585, 335, 388 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, 335, 388 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 335, 388 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, 335, 388 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, 335, 388 is 1.

HCF(585, 335, 388) = 1

HCF of 585, 335, 388 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, 335, 388 is 1.

Highest Common Factor of 585,335,388 using Euclid's algorithm

Highest Common Factor of 585,335,388 is 1

Step 1: Since 585 > 335, we apply the division lemma to 585 and 335, to get

585 = 335 x 1 + 250

Step 2: Since the reminder 335 ≠ 0, we apply division lemma to 250 and 335, to get

335 = 250 x 1 + 85

Step 3: We consider the new divisor 250 and the new remainder 85, and apply the division lemma to get

250 = 85 x 2 + 80

We consider the new divisor 85 and the new remainder 80,and apply the division lemma to get

85 = 80 x 1 + 5

We consider the new divisor 80 and the new remainder 5,and apply the division lemma to get

80 = 5 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 585 and 335 is 5

Notice that 5 = HCF(80,5) = HCF(85,80) = HCF(250,85) = HCF(335,250) = HCF(585,335) .

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

Step 1: Since 388 > 5, we apply the division lemma to 388 and 5, to get

388 = 5 x 77 + 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 388 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(388,5) .

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Frequently Asked Questions on HCF of 585, 335, 388 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, 335, 388?

Answer: HCF of 585, 335, 388 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 335, 388 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 335, 388 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.