Highest Common Factor of 5101, 8227 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 5101, 8227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5101, 8227 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 5101, 8227 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 5101, 8227 is 1.

HCF(5101, 8227) = 1

HCF of 5101, 8227 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 5101, 8227 is 1.

Highest Common Factor of 5101,8227 using Euclid's algorithm

Highest Common Factor of 5101,8227 is 1

Step 1: Since 8227 > 5101, we apply the division lemma to 8227 and 5101, to get

8227 = 5101 x 1 + 3126

Step 2: Since the reminder 5101 ≠ 0, we apply division lemma to 3126 and 5101, to get

5101 = 3126 x 1 + 1975

Step 3: We consider the new divisor 3126 and the new remainder 1975, and apply the division lemma to get

3126 = 1975 x 1 + 1151

We consider the new divisor 1975 and the new remainder 1151,and apply the division lemma to get

1975 = 1151 x 1 + 824

We consider the new divisor 1151 and the new remainder 824,and apply the division lemma to get

1151 = 824 x 1 + 327

We consider the new divisor 824 and the new remainder 327,and apply the division lemma to get

824 = 327 x 2 + 170

We consider the new divisor 327 and the new remainder 170,and apply the division lemma to get

327 = 170 x 1 + 157

We consider the new divisor 170 and the new remainder 157,and apply the division lemma to get

170 = 157 x 1 + 13

We consider the new divisor 157 and the new remainder 13,and apply the division lemma to get

157 = 13 x 12 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5101 and 8227 is 1

Notice that 1 = HCF(13,1) = HCF(157,13) = HCF(170,157) = HCF(327,170) = HCF(824,327) = HCF(1151,824) = HCF(1975,1151) = HCF(3126,1975) = HCF(5101,3126) = HCF(8227,5101) .

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Frequently Asked Questions on HCF of 5101, 8227 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 5101, 8227?

Answer: HCF of 5101, 8227 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5101, 8227 using Euclid's Algorithm?

Answer: For arbitrary numbers 5101, 8227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.