Highest Common Factor of 364, 559, 41 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 364, 559, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 559, 41 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 364, 559, 41 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 364, 559, 41 is 1.

HCF(364, 559, 41) = 1

HCF of 364, 559, 41 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 364, 559, 41 is 1.

Highest Common Factor of 364,559,41 using Euclid's algorithm

Highest Common Factor of 364,559,41 is 1

Step 1: Since 559 > 364, we apply the division lemma to 559 and 364, to get

559 = 364 x 1 + 195

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 195 and 364, to get

364 = 195 x 1 + 169

Step 3: We consider the new divisor 195 and the new remainder 169, and apply the division lemma to get

195 = 169 x 1 + 26

We consider the new divisor 169 and the new remainder 26,and apply the division lemma to get

169 = 26 x 6 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 364 and 559 is 13

Notice that 13 = HCF(26,13) = HCF(169,26) = HCF(195,169) = HCF(364,195) = HCF(559,364) .

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

Step 1: Since 41 > 13, we apply the division lemma to 41 and 13, to get

41 = 13 x 3 + 2

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get

13 = 2 x 6 + 1

Step 3: 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 13 and 41 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) .

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Frequently Asked Questions on HCF of 364, 559, 41 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 364, 559, 41?

Answer: HCF of 364, 559, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 559, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 559, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.