Highest Common Factor of 311, 498, 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 311, 498, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 311, 498, 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 311, 498, 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 311, 498, 41 is 1.

HCF(311, 498, 41) = 1

HCF of 311, 498, 41 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 311, 498, 41 is 1.

Highest Common Factor of 311,498,41 using Euclid's algorithm

Highest Common Factor of 311,498,41 is 1

Step 1: Since 498 > 311, we apply the division lemma to 498 and 311, to get

498 = 311 x 1 + 187

Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 187 and 311, to get

311 = 187 x 1 + 124

Step 3: We consider the new divisor 187 and the new remainder 124, and apply the division lemma to get

187 = 124 x 1 + 63

We consider the new divisor 124 and the new remainder 63,and apply the division lemma to get

124 = 63 x 1 + 61

We consider the new divisor 63 and the new remainder 61,and apply the division lemma to get

63 = 61 x 1 + 2

We consider the new divisor 61 and the new remainder 2,and apply the division lemma to get

61 = 2 x 30 + 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 311 and 498 is 1

Notice that 1 = HCF(2,1) = HCF(61,2) = HCF(63,61) = HCF(124,63) = HCF(187,124) = HCF(311,187) = HCF(498,311) .

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

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

41 = 1 x 41 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41 is 1

Notice that 1 = HCF(41,1) .

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Frequently Asked Questions on HCF of 311, 498, 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 311, 498, 41?

Answer: HCF of 311, 498, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 311, 498, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 311, 498, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.