Highest Common Factor of 419, 5642 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 419, 5642 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 5642 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 419, 5642 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 419, 5642 is 1.

HCF(419, 5642) = 1

HCF of 419, 5642 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 419, 5642 is 1.

Highest Common Factor of 419,5642 using Euclid's algorithm

Highest Common Factor of 419,5642 is 1

Step 1: Since 5642 > 419, we apply the division lemma to 5642 and 419, to get

5642 = 419 x 13 + 195

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 195 and 419, to get

419 = 195 x 2 + 29

Step 3: We consider the new divisor 195 and the new remainder 29, and apply the division lemma to get

195 = 29 x 6 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 419 and 5642 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(195,29) = HCF(419,195) = HCF(5642,419) .

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Frequently Asked Questions on HCF of 419, 5642 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 419, 5642?

Answer: HCF of 419, 5642 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 5642 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 5642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.