Highest Common Factor of 772, 299, 115, 585 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 772, 299, 115, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 772, 299, 115, 585 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 772, 299, 115, 585 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 772, 299, 115, 585 is 1.

HCF(772, 299, 115, 585) = 1

HCF of 772, 299, 115, 585 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 772, 299, 115, 585 is 1.

Highest Common Factor of 772,299,115,585 using Euclid's algorithm

Highest Common Factor of 772,299,115,585 is 1

Step 1: Since 772 > 299, we apply the division lemma to 772 and 299, to get

772 = 299 x 2 + 174

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 174 and 299, to get

299 = 174 x 1 + 125

Step 3: We consider the new divisor 174 and the new remainder 125, and apply the division lemma to get

174 = 125 x 1 + 49

We consider the new divisor 125 and the new remainder 49,and apply the division lemma to get

125 = 49 x 2 + 27

We consider the new divisor 49 and the new remainder 27,and apply the division lemma to get

49 = 27 x 1 + 22

We consider the new divisor 27 and the new remainder 22,and apply the division lemma to get

27 = 22 x 1 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 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 772 and 299 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(27,22) = HCF(49,27) = HCF(125,49) = HCF(174,125) = HCF(299,174) = HCF(772,299) .

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

Step 1: Since 115 > 1, we apply the division lemma to 115 and 1, to get

115 = 1 x 115 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 115 is 1

Notice that 1 = HCF(115,1) .

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

Step 1: Since 585 > 1, we apply the division lemma to 585 and 1, to get

585 = 1 x 585 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 585 is 1

Notice that 1 = HCF(585,1) .

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Frequently Asked Questions on HCF of 772, 299, 115, 585 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 772, 299, 115, 585?

Answer: HCF of 772, 299, 115, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 772, 299, 115, 585 using Euclid's Algorithm?

Answer: For arbitrary numbers 772, 299, 115, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.