Highest Common Factor of 585, 814, 14 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, 814, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 814, 14 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, 814, 14 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, 814, 14 is 1.

HCF(585, 814, 14) = 1

HCF of 585, 814, 14 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, 814, 14 is 1.

Highest Common Factor of 585,814,14 using Euclid's algorithm

Highest Common Factor of 585,814,14 is 1

Step 1: Since 814 > 585, we apply the division lemma to 814 and 585, to get

814 = 585 x 1 + 229

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 229 and 585, to get

585 = 229 x 2 + 127

Step 3: We consider the new divisor 229 and the new remainder 127, and apply the division lemma to get

229 = 127 x 1 + 102

We consider the new divisor 127 and the new remainder 102,and apply the division lemma to get

127 = 102 x 1 + 25

We consider the new divisor 102 and the new remainder 25,and apply the division lemma to get

102 = 25 x 4 + 2

We consider the new divisor 25 and the new remainder 2,and apply the division lemma to get

25 = 2 x 12 + 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 814 is 1

Notice that 1 = HCF(2,1) = HCF(25,2) = HCF(102,25) = HCF(127,102) = HCF(229,127) = HCF(585,229) = HCF(814,585) .

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

Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1

Notice that 1 = HCF(14,1) .

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Frequently Asked Questions on HCF of 585, 814, 14 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, 814, 14?

Answer: HCF of 585, 814, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 814, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 814, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.