Highest Common Factor of 559, 912, 299 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 559, 912, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 559, 912, 299 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 559, 912, 299 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 559, 912, 299 is 1.

HCF(559, 912, 299) = 1

HCF of 559, 912, 299 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 559, 912, 299 is 1.

Highest Common Factor of 559,912,299 using Euclid's algorithm

Highest Common Factor of 559,912,299 is 1

Step 1: Since 912 > 559, we apply the division lemma to 912 and 559, to get

912 = 559 x 1 + 353

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 353 and 559, to get

559 = 353 x 1 + 206

Step 3: We consider the new divisor 353 and the new remainder 206, and apply the division lemma to get

353 = 206 x 1 + 147

We consider the new divisor 206 and the new remainder 147,and apply the division lemma to get

206 = 147 x 1 + 59

We consider the new divisor 147 and the new remainder 59,and apply the division lemma to get

147 = 59 x 2 + 29

We consider the new divisor 59 and the new remainder 29,and apply the division lemma to get

59 = 29 x 2 + 1

We consider the new divisor 29 and the new remainder 1,and apply the division lemma to get

29 = 1 x 29 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 559 and 912 is 1

Notice that 1 = HCF(29,1) = HCF(59,29) = HCF(147,59) = HCF(206,147) = HCF(353,206) = HCF(559,353) = HCF(912,559) .

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

Step 1: Since 299 > 1, we apply the division lemma to 299 and 1, to get

299 = 1 x 299 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 299 is 1

Notice that 1 = HCF(299,1) .

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Frequently Asked Questions on HCF of 559, 912, 299 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 559, 912, 299?

Answer: HCF of 559, 912, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 559, 912, 299 using Euclid's Algorithm?

Answer: For arbitrary numbers 559, 912, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.