Highest Common Factor of 512, 218, 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 512, 218, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 218, 14 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 512, 218, 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 512, 218, 14 is 2.

HCF(512, 218, 14) = 2

HCF of 512, 218, 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 512, 218, 14 is 2.

Highest Common Factor of 512,218,14 using Euclid's algorithm

Highest Common Factor of 512,218,14 is 2

Step 1: Since 512 > 218, we apply the division lemma to 512 and 218, to get

512 = 218 x 2 + 76

Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 76 and 218, to get

218 = 76 x 2 + 66

Step 3: We consider the new divisor 76 and the new remainder 66, and apply the division lemma to get

76 = 66 x 1 + 10

We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get

66 = 10 x 6 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 512 and 218 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(76,66) = HCF(218,76) = HCF(512,218) .

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

Step 1: Since 14 > 2, we apply the division lemma to 14 and 2, to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14 is 2

Notice that 2 = HCF(14,2) .

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Frequently Asked Questions on HCF of 512, 218, 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 512, 218, 14?

Answer: HCF of 512, 218, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 218, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 218, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.