Highest Common Factor of 214, 585, 218 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 214, 585, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 214, 585, 218 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 214, 585, 218 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 214, 585, 218 is 1.

HCF(214, 585, 218) = 1

HCF of 214, 585, 218 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 214, 585, 218 is 1.

Highest Common Factor of 214,585,218 using Euclid's algorithm

Highest Common Factor of 214,585,218 is 1

Step 1: Since 585 > 214, we apply the division lemma to 585 and 214, to get

585 = 214 x 2 + 157

Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 157 and 214, to get

214 = 157 x 1 + 57

Step 3: We consider the new divisor 157 and the new remainder 57, and apply the division lemma to get

157 = 57 x 2 + 43

We consider the new divisor 57 and the new remainder 43,and apply the division lemma to get

57 = 43 x 1 + 14

We consider the new divisor 43 and the new remainder 14,and apply the division lemma to get

43 = 14 x 3 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma 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 214 and 585 is 1

Notice that 1 = HCF(14,1) = HCF(43,14) = HCF(57,43) = HCF(157,57) = HCF(214,157) = HCF(585,214) .

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

Step 1: Since 218 > 1, we apply the division lemma to 218 and 1, to get

218 = 1 x 218 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 218 is 1

Notice that 1 = HCF(218,1) .

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Frequently Asked Questions on HCF of 214, 585, 218 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 214, 585, 218?

Answer: HCF of 214, 585, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 214, 585, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 214, 585, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.