Highest Common Factor of 873, 2485, 2008 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 873, 2485, 2008 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 873, 2485, 2008 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 873, 2485, 2008 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 873, 2485, 2008 is 1.

HCF(873, 2485, 2008) = 1

HCF of 873, 2485, 2008 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 873, 2485, 2008 is 1.

Highest Common Factor of 873,2485,2008 using Euclid's algorithm

Highest Common Factor of 873,2485,2008 is 1

Step 1: Since 2485 > 873, we apply the division lemma to 2485 and 873, to get

2485 = 873 x 2 + 739

Step 2: Since the reminder 873 ≠ 0, we apply division lemma to 739 and 873, to get

873 = 739 x 1 + 134

Step 3: We consider the new divisor 739 and the new remainder 134, and apply the division lemma to get

739 = 134 x 5 + 69

We consider the new divisor 134 and the new remainder 69,and apply the division lemma to get

134 = 69 x 1 + 65

We consider the new divisor 69 and the new remainder 65,and apply the division lemma to get

69 = 65 x 1 + 4

We consider the new divisor 65 and the new remainder 4,and apply the division lemma to get

65 = 4 x 16 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 873 and 2485 is 1

Notice that 1 = HCF(4,1) = HCF(65,4) = HCF(69,65) = HCF(134,69) = HCF(739,134) = HCF(873,739) = HCF(2485,873) .

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

Step 1: Since 2008 > 1, we apply the division lemma to 2008 and 1, to get

2008 = 1 x 2008 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2008 is 1

Notice that 1 = HCF(2008,1) .

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Frequently Asked Questions on HCF of 873, 2485, 2008 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 873, 2485, 2008?

Answer: HCF of 873, 2485, 2008 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 873, 2485, 2008 using Euclid's Algorithm?

Answer: For arbitrary numbers 873, 2485, 2008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.