Highest Common Factor of 549, 209, 689 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 549, 209, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 549, 209, 689 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 549, 209, 689 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 549, 209, 689 is 1.

HCF(549, 209, 689) = 1

HCF of 549, 209, 689 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 549, 209, 689 is 1.

Highest Common Factor of 549,209,689 using Euclid's algorithm

Highest Common Factor of 549,209,689 is 1

Step 1: Since 549 > 209, we apply the division lemma to 549 and 209, to get

549 = 209 x 2 + 131

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 131 and 209, to get

209 = 131 x 1 + 78

Step 3: We consider the new divisor 131 and the new remainder 78, and apply the division lemma to get

131 = 78 x 1 + 53

We consider the new divisor 78 and the new remainder 53,and apply the division lemma to get

78 = 53 x 1 + 25

We consider the new divisor 53 and the new remainder 25,and apply the division lemma to get

53 = 25 x 2 + 3

We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get

25 = 3 x 8 + 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 549 and 209 is 1

Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(53,25) = HCF(78,53) = HCF(131,78) = HCF(209,131) = HCF(549,209) .

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

Step 1: Since 689 > 1, we apply the division lemma to 689 and 1, to get

689 = 1 x 689 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 689 is 1

Notice that 1 = HCF(689,1) .

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Frequently Asked Questions on HCF of 549, 209, 689 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 549, 209, 689?

Answer: HCF of 549, 209, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 549, 209, 689 using Euclid's Algorithm?

Answer: For arbitrary numbers 549, 209, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.