Highest Common Factor of 909, 566, 518 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 909, 566, 518 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 566, 518 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 909, 566, 518 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 909, 566, 518 is 1.

HCF(909, 566, 518) = 1

HCF of 909, 566, 518 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 909, 566, 518 is 1.

Highest Common Factor of 909,566,518 using Euclid's algorithm

Highest Common Factor of 909,566,518 is 1

Step 1: Since 909 > 566, we apply the division lemma to 909 and 566, to get

909 = 566 x 1 + 343

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 343 and 566, to get

566 = 343 x 1 + 223

Step 3: We consider the new divisor 343 and the new remainder 223, and apply the division lemma to get

343 = 223 x 1 + 120

We consider the new divisor 223 and the new remainder 120,and apply the division lemma to get

223 = 120 x 1 + 103

We consider the new divisor 120 and the new remainder 103,and apply the division lemma to get

120 = 103 x 1 + 17

We consider the new divisor 103 and the new remainder 17,and apply the division lemma to get

103 = 17 x 6 + 1

We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get

17 = 1 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 566 is 1

Notice that 1 = HCF(17,1) = HCF(103,17) = HCF(120,103) = HCF(223,120) = HCF(343,223) = HCF(566,343) = HCF(909,566) .

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

Step 1: Since 518 > 1, we apply the division lemma to 518 and 1, to get

518 = 1 x 518 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 518 is 1

Notice that 1 = HCF(518,1) .

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Frequently Asked Questions on HCF of 909, 566, 518 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 909, 566, 518?

Answer: HCF of 909, 566, 518 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 566, 518 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 566, 518 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.