Highest Common Factor of 872, 529, 559 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 872, 529, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 872, 529, 559 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 872, 529, 559 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 872, 529, 559 is 1.

HCF(872, 529, 559) = 1

HCF of 872, 529, 559 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 872, 529, 559 is 1.

Highest Common Factor of 872,529,559 using Euclid's algorithm

Highest Common Factor of 872,529,559 is 1

Step 1: Since 872 > 529, we apply the division lemma to 872 and 529, to get

872 = 529 x 1 + 343

Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 343 and 529, to get

529 = 343 x 1 + 186

Step 3: We consider the new divisor 343 and the new remainder 186, and apply the division lemma to get

343 = 186 x 1 + 157

We consider the new divisor 186 and the new remainder 157,and apply the division lemma to get

186 = 157 x 1 + 29

We consider the new divisor 157 and the new remainder 29,and apply the division lemma to get

157 = 29 x 5 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 872 and 529 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(157,29) = HCF(186,157) = HCF(343,186) = HCF(529,343) = HCF(872,529) .

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

Step 1: Since 559 > 1, we apply the division lemma to 559 and 1, to get

559 = 1 x 559 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 559 is 1

Notice that 1 = HCF(559,1) .

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Frequently Asked Questions on HCF of 872, 529, 559 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 872, 529, 559?

Answer: HCF of 872, 529, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 872, 529, 559 using Euclid's Algorithm?

Answer: For arbitrary numbers 872, 529, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.