Highest Common Factor of 805, 216, 784 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, 216, 784 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 805, 216, 784 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, 216, 784 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, 216, 784 is 1.

HCF(805, 216, 784) = 1

HCF of 805, 216, 784 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, 216, 784 is 1.

Highest Common Factor of 805,216,784 using Euclid's algorithm

Highest Common Factor of 805,216,784 is 1

Step 1: Since 805 > 216, we apply the division lemma to 805 and 216, to get

805 = 216 x 3 + 157

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 157 and 216, to get

216 = 157 x 1 + 59

Step 3: We consider the new divisor 157 and the new remainder 59, and apply the division lemma to get

157 = 59 x 2 + 39

We consider the new divisor 59 and the new remainder 39,and apply the division lemma to get

59 = 39 x 1 + 20

We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get

39 = 20 x 1 + 19

We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get

20 = 19 x 1 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 805 and 216 is 1

Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(59,39) = HCF(157,59) = HCF(216,157) = HCF(805,216) .

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

Step 1: Since 784 > 1, we apply the division lemma to 784 and 1, to get

784 = 1 x 784 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 784 is 1

Notice that 1 = HCF(784,1) .

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Frequently Asked Questions on HCF of 805, 216, 784 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, 216, 784?

Answer: HCF of 805, 216, 784 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 805, 216, 784 using Euclid's Algorithm?

Answer: For arbitrary numbers 805, 216, 784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.