Highest Common Factor of 508, 214 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 508, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 214 is 2 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 508, 214 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 508, 214 is 2.

HCF(508, 214) = 2

HCF of 508, 214 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 508, 214 is 2.

Highest Common Factor of 508,214 using Euclid's algorithm

Highest Common Factor of 508,214 is 2

Step 1: Since 508 > 214, we apply the division lemma to 508 and 214, to get

508 = 214 x 2 + 80

Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 80 and 214, to get

214 = 80 x 2 + 54

Step 3: We consider the new divisor 80 and the new remainder 54, and apply the division lemma to get

80 = 54 x 1 + 26

We consider the new divisor 54 and the new remainder 26,and apply the division lemma to get

54 = 26 x 2 + 2

We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get

26 = 2 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 508 and 214 is 2

Notice that 2 = HCF(26,2) = HCF(54,26) = HCF(80,54) = HCF(214,80) = HCF(508,214) .

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Frequently Asked Questions on HCF of 508, 214 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 508, 214?

Answer: HCF of 508, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 214 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.