Highest Common Factor of 509, 189, 208 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 509, 189, 208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 189, 208 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 509, 189, 208 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 509, 189, 208 is 1.

HCF(509, 189, 208) = 1

HCF of 509, 189, 208 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 509, 189, 208 is 1.

Highest Common Factor of 509,189,208 using Euclid's algorithm

Highest Common Factor of 509,189,208 is 1

Step 1: Since 509 > 189, we apply the division lemma to 509 and 189, to get

509 = 189 x 2 + 131

Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 131 and 189, to get

189 = 131 x 1 + 58

Step 3: We consider the new divisor 131 and the new remainder 58, and apply the division lemma to get

131 = 58 x 2 + 15

We consider the new divisor 58 and the new remainder 15,and apply the division lemma to get

58 = 15 x 3 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 509 and 189 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(58,15) = HCF(131,58) = HCF(189,131) = HCF(509,189) .

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

Step 1: Since 208 > 1, we apply the division lemma to 208 and 1, to get

208 = 1 x 208 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 208 is 1

Notice that 1 = HCF(208,1) .

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Frequently Asked Questions on HCF of 509, 189, 208 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 509, 189, 208?

Answer: HCF of 509, 189, 208 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 189, 208 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 189, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.