Highest Common Factor of 204, 575, 116 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 204, 575, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 204, 575, 116 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 204, 575, 116 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 204, 575, 116 is 1.

HCF(204, 575, 116) = 1

HCF of 204, 575, 116 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 204, 575, 116 is 1.

Highest Common Factor of 204,575,116 using Euclid's algorithm

Highest Common Factor of 204,575,116 is 1

Step 1: Since 575 > 204, we apply the division lemma to 575 and 204, to get

575 = 204 x 2 + 167

Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 167 and 204, to get

204 = 167 x 1 + 37

Step 3: We consider the new divisor 167 and the new remainder 37, and apply the division lemma to get

167 = 37 x 4 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 204 and 575 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(167,37) = HCF(204,167) = HCF(575,204) .

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

Step 1: Since 116 > 1, we apply the division lemma to 116 and 1, to get

116 = 1 x 116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 116 is 1

Notice that 1 = HCF(116,1) .

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Frequently Asked Questions on HCF of 204, 575, 116 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 204, 575, 116?

Answer: HCF of 204, 575, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 204, 575, 116 using Euclid's Algorithm?

Answer: For arbitrary numbers 204, 575, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.