Highest Common Factor of 827, 5340, 6505 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 827, 5340, 6505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 5340, 6505 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 827, 5340, 6505 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 827, 5340, 6505 is 1.

HCF(827, 5340, 6505) = 1

HCF of 827, 5340, 6505 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 827, 5340, 6505 is 1.

Highest Common Factor of 827,5340,6505 using Euclid's algorithm

Highest Common Factor of 827,5340,6505 is 1

Step 1: Since 5340 > 827, we apply the division lemma to 5340 and 827, to get

5340 = 827 x 6 + 378

Step 2: Since the reminder 827 ≠ 0, we apply division lemma to 378 and 827, to get

827 = 378 x 2 + 71

Step 3: We consider the new divisor 378 and the new remainder 71, and apply the division lemma to get

378 = 71 x 5 + 23

We consider the new divisor 71 and the new remainder 23,and apply the division lemma to get

71 = 23 x 3 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 827 and 5340 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(71,23) = HCF(378,71) = HCF(827,378) = HCF(5340,827) .

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

Step 1: Since 6505 > 1, we apply the division lemma to 6505 and 1, to get

6505 = 1 x 6505 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6505 is 1

Notice that 1 = HCF(6505,1) .

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Frequently Asked Questions on HCF of 827, 5340, 6505 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 827, 5340, 6505?

Answer: HCF of 827, 5340, 6505 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 5340, 6505 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 5340, 6505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.