Highest Common Factor of 800, 585, 117 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 800, 585, 117 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 800, 585, 117 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 800, 585, 117 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 800, 585, 117 is 1.

HCF(800, 585, 117) = 1

HCF of 800, 585, 117 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 800, 585, 117 is 1.

Highest Common Factor of 800,585,117 using Euclid's algorithm

Highest Common Factor of 800,585,117 is 1

Step 1: Since 800 > 585, we apply the division lemma to 800 and 585, to get

800 = 585 x 1 + 215

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 215 and 585, to get

585 = 215 x 2 + 155

Step 3: We consider the new divisor 215 and the new remainder 155, and apply the division lemma to get

215 = 155 x 1 + 60

We consider the new divisor 155 and the new remainder 60,and apply the division lemma to get

155 = 60 x 2 + 35

We consider the new divisor 60 and the new remainder 35,and apply the division lemma to get

60 = 35 x 1 + 25

We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get

35 = 25 x 1 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 800 and 585 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(155,60) = HCF(215,155) = HCF(585,215) = HCF(800,585) .

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

Step 1: Since 117 > 5, we apply the division lemma to 117 and 5, to get

117 = 5 x 23 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: 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 5 and 117 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(117,5) .

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Frequently Asked Questions on HCF of 800, 585, 117 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 800, 585, 117?

Answer: HCF of 800, 585, 117 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 800, 585, 117 using Euclid's Algorithm?

Answer: For arbitrary numbers 800, 585, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.