Highest Common Factor of 504, 866, 213 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 504, 866, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 504, 866, 213 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 504, 866, 213 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 504, 866, 213 is 1.

HCF(504, 866, 213) = 1

HCF of 504, 866, 213 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 504, 866, 213 is 1.

Highest Common Factor of 504,866,213 using Euclid's algorithm

Highest Common Factor of 504,866,213 is 1

Step 1: Since 866 > 504, we apply the division lemma to 866 and 504, to get

866 = 504 x 1 + 362

Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 362 and 504, to get

504 = 362 x 1 + 142

Step 3: We consider the new divisor 362 and the new remainder 142, and apply the division lemma to get

362 = 142 x 2 + 78

We consider the new divisor 142 and the new remainder 78,and apply the division lemma to get

142 = 78 x 1 + 64

We consider the new divisor 78 and the new remainder 64,and apply the division lemma to get

78 = 64 x 1 + 14

We consider the new divisor 64 and the new remainder 14,and apply the division lemma to get

64 = 14 x 4 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 504 and 866 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(64,14) = HCF(78,64) = HCF(142,78) = HCF(362,142) = HCF(504,362) = HCF(866,504) .

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

Step 1: Since 213 > 2, we apply the division lemma to 213 and 2, to get

213 = 2 x 106 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 213 is 1

Notice that 1 = HCF(2,1) = HCF(213,2) .

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Frequently Asked Questions on HCF of 504, 866, 213 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 504, 866, 213?

Answer: HCF of 504, 866, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 504, 866, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 504, 866, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.