Highest Common Factor of 6503, 2306 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 6503, 2306 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6503, 2306 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 6503, 2306 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 6503, 2306 is 1.

HCF(6503, 2306) = 1

HCF of 6503, 2306 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 6503, 2306 is 1.

Highest Common Factor of 6503,2306 using Euclid's algorithm

Highest Common Factor of 6503,2306 is 1

Step 1: Since 6503 > 2306, we apply the division lemma to 6503 and 2306, to get

6503 = 2306 x 2 + 1891

Step 2: Since the reminder 2306 ≠ 0, we apply division lemma to 1891 and 2306, to get

2306 = 1891 x 1 + 415

Step 3: We consider the new divisor 1891 and the new remainder 415, and apply the division lemma to get

1891 = 415 x 4 + 231

We consider the new divisor 415 and the new remainder 231,and apply the division lemma to get

415 = 231 x 1 + 184

We consider the new divisor 231 and the new remainder 184,and apply the division lemma to get

231 = 184 x 1 + 47

We consider the new divisor 184 and the new remainder 47,and apply the division lemma to get

184 = 47 x 3 + 43

We consider the new divisor 47 and the new remainder 43,and apply the division lemma to get

47 = 43 x 1 + 4

We consider the new divisor 43 and the new remainder 4,and apply the division lemma to get

43 = 4 x 10 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6503 and 2306 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(43,4) = HCF(47,43) = HCF(184,47) = HCF(231,184) = HCF(415,231) = HCF(1891,415) = HCF(2306,1891) = HCF(6503,2306) .

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Frequently Asked Questions on HCF of 6503, 2306 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 6503, 2306?

Answer: HCF of 6503, 2306 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6503, 2306 using Euclid's Algorithm?

Answer: For arbitrary numbers 6503, 2306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.