Highest Common Factor of 854, 541, 60, 391 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 854, 541, 60, 391 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 541, 60, 391 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 854, 541, 60, 391 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 854, 541, 60, 391 is 1.

HCF(854, 541, 60, 391) = 1

HCF of 854, 541, 60, 391 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 854, 541, 60, 391 is 1.

Highest Common Factor of 854,541,60,391 using Euclid's algorithm

Highest Common Factor of 854,541,60,391 is 1

Step 1: Since 854 > 541, we apply the division lemma to 854 and 541, to get

854 = 541 x 1 + 313

Step 2: Since the reminder 541 ≠ 0, we apply division lemma to 313 and 541, to get

541 = 313 x 1 + 228

Step 3: We consider the new divisor 313 and the new remainder 228, and apply the division lemma to get

313 = 228 x 1 + 85

We consider the new divisor 228 and the new remainder 85,and apply the division lemma to get

228 = 85 x 2 + 58

We consider the new divisor 85 and the new remainder 58,and apply the division lemma to get

85 = 58 x 1 + 27

We consider the new divisor 58 and the new remainder 27,and apply the division lemma to get

58 = 27 x 2 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 854 and 541 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(58,27) = HCF(85,58) = HCF(228,85) = HCF(313,228) = HCF(541,313) = HCF(854,541) .

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

Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get

60 = 1 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1

Notice that 1 = HCF(60,1) .

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

Step 1: Since 391 > 1, we apply the division lemma to 391 and 1, to get

391 = 1 x 391 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 391 is 1

Notice that 1 = HCF(391,1) .

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Frequently Asked Questions on HCF of 854, 541, 60, 391 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 854, 541, 60, 391?

Answer: HCF of 854, 541, 60, 391 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 541, 60, 391 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 541, 60, 391 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.