Highest Common Factor of 420, 805, 445, 863 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, 805, 445, 863 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 805, 445, 863 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, 805, 445, 863 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, 805, 445, 863 is 1.

HCF(420, 805, 445, 863) = 1

HCF of 420, 805, 445, 863 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, 805, 445, 863 is 1.

Highest Common Factor of 420,805,445,863 using Euclid's algorithm

Highest Common Factor of 420,805,445,863 is 1

Step 1: Since 805 > 420, we apply the division lemma to 805 and 420, to get

805 = 420 x 1 + 385

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 385 and 420, to get

420 = 385 x 1 + 35

Step 3: We consider the new divisor 385 and the new remainder 35, and apply the division lemma to get

385 = 35 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 420 and 805 is 35

Notice that 35 = HCF(385,35) = HCF(420,385) = HCF(805,420) .

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

Step 1: Since 445 > 35, we apply the division lemma to 445 and 35, to get

445 = 35 x 12 + 25

Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 25 and 35, to get

35 = 25 x 1 + 10

Step 3: We consider the new divisor 25 and the new remainder 10, and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 35 and 445 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(445,35) .

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

Step 1: Since 863 > 5, we apply the division lemma to 863 and 5, to get

863 = 5 x 172 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 863 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(863,5) .

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Frequently Asked Questions on HCF of 420, 805, 445, 863 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, 805, 445, 863?

Answer: HCF of 420, 805, 445, 863 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 805, 445, 863 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 805, 445, 863 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.