Highest Common Factor of 5045, 5312 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 5045, 5312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5045, 5312 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 5045, 5312 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 5045, 5312 is 1.

HCF(5045, 5312) = 1

HCF of 5045, 5312 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 5045, 5312 is 1.

Highest Common Factor of 5045,5312 using Euclid's algorithm

Highest Common Factor of 5045,5312 is 1

Step 1: Since 5312 > 5045, we apply the division lemma to 5312 and 5045, to get

5312 = 5045 x 1 + 267

Step 2: Since the reminder 5045 ≠ 0, we apply division lemma to 267 and 5045, to get

5045 = 267 x 18 + 239

Step 3: We consider the new divisor 267 and the new remainder 239, and apply the division lemma to get

267 = 239 x 1 + 28

We consider the new divisor 239 and the new remainder 28,and apply the division lemma to get

239 = 28 x 8 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 5045 and 5312 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(239,28) = HCF(267,239) = HCF(5045,267) = HCF(5312,5045) .

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Frequently Asked Questions on HCF of 5045, 5312 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 5045, 5312?

Answer: HCF of 5045, 5312 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5045, 5312 using Euclid's Algorithm?

Answer: For arbitrary numbers 5045, 5312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.