Highest Common Factor of 419, 675, 814 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, 675, 814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 675, 814 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, 675, 814 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, 675, 814 is 1.

HCF(419, 675, 814) = 1

HCF of 419, 675, 814 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, 675, 814 is 1.

Highest Common Factor of 419,675,814 using Euclid's algorithm

Highest Common Factor of 419,675,814 is 1

Step 1: Since 675 > 419, we apply the division lemma to 675 and 419, to get

675 = 419 x 1 + 256

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 256 and 419, to get

419 = 256 x 1 + 163

Step 3: We consider the new divisor 256 and the new remainder 163, and apply the division lemma to get

256 = 163 x 1 + 93

We consider the new divisor 163 and the new remainder 93,and apply the division lemma to get

163 = 93 x 1 + 70

We consider the new divisor 93 and the new remainder 70,and apply the division lemma to get

93 = 70 x 1 + 23

We consider the new divisor 70 and the new remainder 23,and apply the division lemma to get

70 = 23 x 3 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 675 is 1

Notice that 1 = HCF(23,1) = HCF(70,23) = HCF(93,70) = HCF(163,93) = HCF(256,163) = HCF(419,256) = HCF(675,419) .

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

Step 1: Since 814 > 1, we apply the division lemma to 814 and 1, to get

814 = 1 x 814 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 814 is 1

Notice that 1 = HCF(814,1) .

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Frequently Asked Questions on HCF of 419, 675, 814 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, 675, 814?

Answer: HCF of 419, 675, 814 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 675, 814 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 675, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.