Highest Common Factor of 800, 414, 641 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 800, 414, 641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 800, 414, 641 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 800, 414, 641 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 800, 414, 641 is 1.

HCF(800, 414, 641) = 1

HCF of 800, 414, 641 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 800, 414, 641 is 1.

Highest Common Factor of 800,414,641 using Euclid's algorithm

Highest Common Factor of 800,414,641 is 1

Step 1: Since 800 > 414, we apply the division lemma to 800 and 414, to get

800 = 414 x 1 + 386

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 386 and 414, to get

414 = 386 x 1 + 28

Step 3: We consider the new divisor 386 and the new remainder 28, and apply the division lemma to get

386 = 28 x 13 + 22

We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get

28 = 22 x 1 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 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 800 and 414 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(386,28) = HCF(414,386) = HCF(800,414) .

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

Step 1: Since 641 > 2, we apply the division lemma to 641 and 2, to get

641 = 2 x 320 + 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 641 is 1

Notice that 1 = HCF(2,1) = HCF(641,2) .

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Frequently Asked Questions on HCF of 800, 414, 641 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 800, 414, 641?

Answer: HCF of 800, 414, 641 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 800, 414, 641 using Euclid's Algorithm?

Answer: For arbitrary numbers 800, 414, 641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.