Highest Common Factor of 420, 2798, 8443 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 420, 2798, 8443 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 2798, 8443 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 420, 2798, 8443 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 420, 2798, 8443 is 1.

HCF(420, 2798, 8443) = 1

HCF of 420, 2798, 8443 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 420, 2798, 8443 is 1.

Highest Common Factor of 420,2798,8443 using Euclid's algorithm

Highest Common Factor of 420,2798,8443 is 1

Step 1: Since 2798 > 420, we apply the division lemma to 2798 and 420, to get

2798 = 420 x 6 + 278

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 278 and 420, to get

420 = 278 x 1 + 142

Step 3: We consider the new divisor 278 and the new remainder 142, and apply the division lemma to get

278 = 142 x 1 + 136

We consider the new divisor 142 and the new remainder 136,and apply the division lemma to get

142 = 136 x 1 + 6

We consider the new divisor 136 and the new remainder 6,and apply the division lemma to get

136 = 6 x 22 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 420 and 2798 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(136,6) = HCF(142,136) = HCF(278,142) = HCF(420,278) = HCF(2798,420) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 8443 > 2, we apply the division lemma to 8443 and 2, to get

8443 = 2 x 4221 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 8443 is 1

Notice that 1 = HCF(2,1) = HCF(8443,2) .

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Frequently Asked Questions on HCF of 420, 2798, 8443 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 420, 2798, 8443?

Answer: HCF of 420, 2798, 8443 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 2798, 8443 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 2798, 8443 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.