Highest Common Factor of 204, 578, 89, 313 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, 578, 89, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 204, 578, 89, 313 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, 578, 89, 313 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, 578, 89, 313 is 1.

HCF(204, 578, 89, 313) = 1

HCF of 204, 578, 89, 313 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, 578, 89, 313 is 1.

Highest Common Factor of 204,578,89,313 using Euclid's algorithm

Highest Common Factor of 204,578,89,313 is 1

Step 1: Since 578 > 204, we apply the division lemma to 578 and 204, to get

578 = 204 x 2 + 170

Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 170 and 204, to get

204 = 170 x 1 + 34

Step 3: We consider the new divisor 170 and the new remainder 34, and apply the division lemma to get

170 = 34 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 204 and 578 is 34

Notice that 34 = HCF(170,34) = HCF(204,170) = HCF(578,204) .

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

Step 1: Since 89 > 34, we apply the division lemma to 89 and 34, to get

89 = 34 x 2 + 21

Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 21 and 34, to get

34 = 21 x 1 + 13

Step 3: We consider the new divisor 21 and the new remainder 13, and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 34 and 89 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(89,34) .

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

Step 1: Since 313 > 1, we apply the division lemma to 313 and 1, to get

313 = 1 x 313 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 313 is 1

Notice that 1 = HCF(313,1) .

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Frequently Asked Questions on HCF of 204, 578, 89, 313 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, 578, 89, 313?

Answer: HCF of 204, 578, 89, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 204, 578, 89, 313 using Euclid's Algorithm?

Answer: For arbitrary numbers 204, 578, 89, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.