Highest Common Factor of 503, 815 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 503, 815 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 503, 815 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 503, 815 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 503, 815 is 1.

HCF(503, 815) = 1

HCF of 503, 815 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 503, 815 is 1.

Highest Common Factor of 503,815 using Euclid's algorithm

Highest Common Factor of 503,815 is 1

Step 1: Since 815 > 503, we apply the division lemma to 815 and 503, to get

815 = 503 x 1 + 312

Step 2: Since the reminder 503 ≠ 0, we apply division lemma to 312 and 503, to get

503 = 312 x 1 + 191

Step 3: We consider the new divisor 312 and the new remainder 191, and apply the division lemma to get

312 = 191 x 1 + 121

We consider the new divisor 191 and the new remainder 121,and apply the division lemma to get

191 = 121 x 1 + 70

We consider the new divisor 121 and the new remainder 70,and apply the division lemma to get

121 = 70 x 1 + 51

We consider the new divisor 70 and the new remainder 51,and apply the division lemma to get

70 = 51 x 1 + 19

We consider the new divisor 51 and the new remainder 19,and apply the division lemma to get

51 = 19 x 2 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 503 and 815 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(51,19) = HCF(70,51) = HCF(121,70) = HCF(191,121) = HCF(312,191) = HCF(503,312) = HCF(815,503) .

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Frequently Asked Questions on HCF of 503, 815 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 503, 815?

Answer: HCF of 503, 815 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 503, 815 using Euclid's Algorithm?

Answer: For arbitrary numbers 503, 815 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.