Highest Common Factor of 809, 209, 25 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 809, 209, 25 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 809, 209, 25 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 809, 209, 25 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 809, 209, 25 is 1.

HCF(809, 209, 25) = 1

HCF of 809, 209, 25 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 809, 209, 25 is 1.

Highest Common Factor of 809,209,25 using Euclid's algorithm

Highest Common Factor of 809,209,25 is 1

Step 1: Since 809 > 209, we apply the division lemma to 809 and 209, to get

809 = 209 x 3 + 182

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 182 and 209, to get

209 = 182 x 1 + 27

Step 3: We consider the new divisor 182 and the new remainder 27, and apply the division lemma to get

182 = 27 x 6 + 20

We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get

27 = 20 x 1 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 809 and 209 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(182,27) = HCF(209,182) = HCF(809,209) .

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

Step 1: Since 25 > 1, we apply the division lemma to 25 and 1, to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 25 is 1

Notice that 1 = HCF(25,1) .

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Frequently Asked Questions on HCF of 809, 209, 25 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 809, 209, 25?

Answer: HCF of 809, 209, 25 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 809, 209, 25 using Euclid's Algorithm?

Answer: For arbitrary numbers 809, 209, 25 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.