Highest Common Factor of 805, 221, 806 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 805, 221, 806 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 805, 221, 806 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 805, 221, 806 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 805, 221, 806 is 1.

HCF(805, 221, 806) = 1

HCF of 805, 221, 806 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 805, 221, 806 is 1.

Highest Common Factor of 805,221,806 using Euclid's algorithm

Highest Common Factor of 805,221,806 is 1

Step 1: Since 805 > 221, we apply the division lemma to 805 and 221, to get

805 = 221 x 3 + 142

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 142 and 221, to get

221 = 142 x 1 + 79

Step 3: We consider the new divisor 142 and the new remainder 79, and apply the division lemma to get

142 = 79 x 1 + 63

We consider the new divisor 79 and the new remainder 63,and apply the division lemma to get

79 = 63 x 1 + 16

We consider the new divisor 63 and the new remainder 16,and apply the division lemma to get

63 = 16 x 3 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 805 and 221 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(63,16) = HCF(79,63) = HCF(142,79) = HCF(221,142) = HCF(805,221) .

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

Step 1: Since 806 > 1, we apply the division lemma to 806 and 1, to get

806 = 1 x 806 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 806 is 1

Notice that 1 = HCF(806,1) .

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Frequently Asked Questions on HCF of 805, 221, 806 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 805, 221, 806?

Answer: HCF of 805, 221, 806 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 805, 221, 806 using Euclid's Algorithm?

Answer: For arbitrary numbers 805, 221, 806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.