Highest Common Factor of 500, 800, 691 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 500, 800, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 500, 800, 691 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 500, 800, 691 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 500, 800, 691 is 1.

HCF(500, 800, 691) = 1

HCF of 500, 800, 691 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 500, 800, 691 is 1.

Highest Common Factor of 500,800,691 using Euclid's algorithm

Highest Common Factor of 500,800,691 is 1

Step 1: Since 800 > 500, we apply the division lemma to 800 and 500, to get

800 = 500 x 1 + 300

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 300 and 500, to get

500 = 300 x 1 + 200

Step 3: We consider the new divisor 300 and the new remainder 200, and apply the division lemma to get

300 = 200 x 1 + 100

We consider the new divisor 200 and the new remainder 100, and apply the division lemma to get

200 = 100 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 100, the HCF of 500 and 800 is 100

Notice that 100 = HCF(200,100) = HCF(300,200) = HCF(500,300) = HCF(800,500) .

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

Step 1: Since 691 > 100, we apply the division lemma to 691 and 100, to get

691 = 100 x 6 + 91

Step 2: Since the reminder 100 ≠ 0, we apply division lemma to 91 and 100, to get

100 = 91 x 1 + 9

Step 3: We consider the new divisor 91 and the new remainder 9, and apply the division lemma to get

91 = 9 x 10 + 1

We consider the new divisor 9 and the new remainder 1, and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 100 and 691 is 1

Notice that 1 = HCF(9,1) = HCF(91,9) = HCF(100,91) = HCF(691,100) .

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Frequently Asked Questions on HCF of 500, 800, 691 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 500, 800, 691?

Answer: HCF of 500, 800, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 500, 800, 691 using Euclid's Algorithm?

Answer: For arbitrary numbers 500, 800, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.