Highest Common Factor of 900, 817, 516 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 900, 817, 516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 817, 516 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 900, 817, 516 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 900, 817, 516 is 1.

HCF(900, 817, 516) = 1

HCF of 900, 817, 516 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 900, 817, 516 is 1.

Highest Common Factor of 900,817,516 using Euclid's algorithm

Highest Common Factor of 900,817,516 is 1

Step 1: Since 900 > 817, we apply the division lemma to 900 and 817, to get

900 = 817 x 1 + 83

Step 2: Since the reminder 817 ≠ 0, we apply division lemma to 83 and 817, to get

817 = 83 x 9 + 70

Step 3: We consider the new divisor 83 and the new remainder 70, and apply the division lemma to get

83 = 70 x 1 + 13

We consider the new divisor 70 and the new remainder 13,and apply the division lemma to get

70 = 13 x 5 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 900 and 817 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(70,13) = HCF(83,70) = HCF(817,83) = HCF(900,817) .

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

Step 1: Since 516 > 1, we apply the division lemma to 516 and 1, to get

516 = 1 x 516 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 516 is 1

Notice that 1 = HCF(516,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 900, 817, 516 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 900, 817, 516?

Answer: HCF of 900, 817, 516 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 817, 516 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 817, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.