Highest Common Factor of 8221, 5454 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 8221, 5454 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8221, 5454 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 8221, 5454 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 8221, 5454 is 1.

HCF(8221, 5454) = 1

HCF of 8221, 5454 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 8221, 5454 is 1.

Highest Common Factor of 8221,5454 using Euclid's algorithm

Highest Common Factor of 8221,5454 is 1

Step 1: Since 8221 > 5454, we apply the division lemma to 8221 and 5454, to get

8221 = 5454 x 1 + 2767

Step 2: Since the reminder 5454 ≠ 0, we apply division lemma to 2767 and 5454, to get

5454 = 2767 x 1 + 2687

Step 3: We consider the new divisor 2767 and the new remainder 2687, and apply the division lemma to get

2767 = 2687 x 1 + 80

We consider the new divisor 2687 and the new remainder 80,and apply the division lemma to get

2687 = 80 x 33 + 47

We consider the new divisor 80 and the new remainder 47,and apply the division lemma to get

80 = 47 x 1 + 33

We consider the new divisor 47 and the new remainder 33,and apply the division lemma to get

47 = 33 x 1 + 14

We consider the new divisor 33 and the new remainder 14,and apply the division lemma to get

33 = 14 x 2 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8221 and 5454 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(33,14) = HCF(47,33) = HCF(80,47) = HCF(2687,80) = HCF(2767,2687) = HCF(5454,2767) = HCF(8221,5454) .

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Frequently Asked Questions on HCF of 8221, 5454 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 8221, 5454?

Answer: HCF of 8221, 5454 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8221, 5454 using Euclid's Algorithm?

Answer: For arbitrary numbers 8221, 5454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.