Highest Common Factor of 198, 541, 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 198, 541, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 198, 541, 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 198, 541, 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 198, 541, 41 is 1.

HCF(198, 541, 41) = 1

HCF of 198, 541, 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 198, 541, 41 is 1.

Highest Common Factor of 198,541,41 using Euclid's algorithm

Highest Common Factor of 198,541,41 is 1

Step 1: Since 541 > 198, we apply the division lemma to 541 and 198, to get

541 = 198 x 2 + 145

Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 145 and 198, to get

198 = 145 x 1 + 53

Step 3: We consider the new divisor 145 and the new remainder 53, and apply the division lemma to get

145 = 53 x 2 + 39

We consider the new divisor 53 and the new remainder 39,and apply the division lemma to get

53 = 39 x 1 + 14

We consider the new divisor 39 and the new remainder 14,and apply the division lemma to get

39 = 14 x 2 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 198 and 541 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(39,14) = HCF(53,39) = HCF(145,53) = HCF(198,145) = HCF(541,198) .

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 198, 541, 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 198, 541, 41?

Answer: HCF of 198, 541, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 198, 541, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 198, 541, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.