Highest Common Factor of 574, 968, 549 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 574, 968, 549 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 574, 968, 549 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 574, 968, 549 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 574, 968, 549 is 1.

HCF(574, 968, 549) = 1

HCF of 574, 968, 549 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 574, 968, 549 is 1.

Highest Common Factor of 574,968,549 using Euclid's algorithm

Highest Common Factor of 574,968,549 is 1

Step 1: Since 968 > 574, we apply the division lemma to 968 and 574, to get

968 = 574 x 1 + 394

Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 394 and 574, to get

574 = 394 x 1 + 180

Step 3: We consider the new divisor 394 and the new remainder 180, and apply the division lemma to get

394 = 180 x 2 + 34

We consider the new divisor 180 and the new remainder 34,and apply the division lemma to get

180 = 34 x 5 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 574 and 968 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(180,34) = HCF(394,180) = HCF(574,394) = HCF(968,574) .

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

Step 1: Since 549 > 2, we apply the division lemma to 549 and 2, to get

549 = 2 x 274 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 549 is 1

Notice that 1 = HCF(2,1) = HCF(549,2) .

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Frequently Asked Questions on HCF of 574, 968, 549 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 574, 968, 549?

Answer: HCF of 574, 968, 549 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 574, 968, 549 using Euclid's Algorithm?

Answer: For arbitrary numbers 574, 968, 549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.