Highest Common Factor of 817, 506, 905 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 817, 506, 905 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 817, 506, 905 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 817, 506, 905 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 817, 506, 905 is 1.

HCF(817, 506, 905) = 1

HCF of 817, 506, 905 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 817, 506, 905 is 1.

Highest Common Factor of 817,506,905 using Euclid's algorithm

Highest Common Factor of 817,506,905 is 1

Step 1: Since 817 > 506, we apply the division lemma to 817 and 506, to get

817 = 506 x 1 + 311

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 311 and 506, to get

506 = 311 x 1 + 195

Step 3: We consider the new divisor 311 and the new remainder 195, and apply the division lemma to get

311 = 195 x 1 + 116

We consider the new divisor 195 and the new remainder 116,and apply the division lemma to get

195 = 116 x 1 + 79

We consider the new divisor 116 and the new remainder 79,and apply the division lemma to get

116 = 79 x 1 + 37

We consider the new divisor 79 and the new remainder 37,and apply the division lemma to get

79 = 37 x 2 + 5

We consider the new divisor 37 and the new remainder 5,and apply the division lemma to get

37 = 5 x 7 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 817 and 506 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(37,5) = HCF(79,37) = HCF(116,79) = HCF(195,116) = HCF(311,195) = HCF(506,311) = HCF(817,506) .

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

Step 1: Since 905 > 1, we apply the division lemma to 905 and 1, to get

905 = 1 x 905 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 905 is 1

Notice that 1 = HCF(905,1) .

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Frequently Asked Questions on HCF of 817, 506, 905 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 817, 506, 905?

Answer: HCF of 817, 506, 905 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 817, 506, 905 using Euclid's Algorithm?

Answer: For arbitrary numbers 817, 506, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.