Highest Common Factor of 209, 266, 32 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 209, 266, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 209, 266, 32 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 209, 266, 32 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 209, 266, 32 is 1.

HCF(209, 266, 32) = 1

HCF of 209, 266, 32 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 209, 266, 32 is 1.

Highest Common Factor of 209,266,32 using Euclid's algorithm

Highest Common Factor of 209,266,32 is 1

Step 1: Since 266 > 209, we apply the division lemma to 266 and 209, to get

266 = 209 x 1 + 57

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 57 and 209, to get

209 = 57 x 3 + 38

Step 3: We consider the new divisor 57 and the new remainder 38, and apply the division lemma to get

57 = 38 x 1 + 19

We consider the new divisor 38 and the new remainder 19, and apply the division lemma to get

38 = 19 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 209 and 266 is 19

Notice that 19 = HCF(38,19) = HCF(57,38) = HCF(209,57) = HCF(266,209) .

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

Step 1: Since 32 > 19, we apply the division lemma to 32 and 19, to get

32 = 19 x 1 + 13

Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 13 and 19, to get

19 = 13 x 1 + 6

Step 3: We consider the new divisor 13 and the new remainder 6, and apply the division lemma to get

13 = 6 x 2 + 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 19 and 32 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) .

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Frequently Asked Questions on HCF of 209, 266, 32 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 209, 266, 32?

Answer: HCF of 209, 266, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 209, 266, 32 using Euclid's Algorithm?

Answer: For arbitrary numbers 209, 266, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.