Highest Common Factor of 827, 584, 514, 684 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, 584, 514, 684 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 584, 514, 684 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, 584, 514, 684 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, 584, 514, 684 is 1.

HCF(827, 584, 514, 684) = 1

HCF of 827, 584, 514, 684 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, 584, 514, 684 is 1.

Highest Common Factor of 827,584,514,684 using Euclid's algorithm

Highest Common Factor of 827,584,514,684 is 1

Step 1: Since 827 > 584, we apply the division lemma to 827 and 584, to get

827 = 584 x 1 + 243

Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 243 and 584, to get

584 = 243 x 2 + 98

Step 3: We consider the new divisor 243 and the new remainder 98, and apply the division lemma to get

243 = 98 x 2 + 47

We consider the new divisor 98 and the new remainder 47,and apply the division lemma to get

98 = 47 x 2 + 4

We consider the new divisor 47 and the new remainder 4,and apply the division lemma to get

47 = 4 x 11 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 827 and 584 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(47,4) = HCF(98,47) = HCF(243,98) = HCF(584,243) = HCF(827,584) .

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

Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get

514 = 1 x 514 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1

Notice that 1 = HCF(514,1) .

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

Step 1: Since 684 > 1, we apply the division lemma to 684 and 1, to get

684 = 1 x 684 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 684 is 1

Notice that 1 = HCF(684,1) .

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Frequently Asked Questions on HCF of 827, 584, 514, 684 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, 584, 514, 684?

Answer: HCF of 827, 584, 514, 684 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 584, 514, 684 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 584, 514, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.