Highest Common Factor of 268, 338, 173 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 268, 338, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 268, 338, 173 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 268, 338, 173 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 268, 338, 173 is 1.

HCF(268, 338, 173) = 1

HCF of 268, 338, 173 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 268, 338, 173 is 1.

Highest Common Factor of 268,338,173 using Euclid's algorithm

Highest Common Factor of 268,338,173 is 1

Step 1: Since 338 > 268, we apply the division lemma to 338 and 268, to get

338 = 268 x 1 + 70

Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 70 and 268, to get

268 = 70 x 3 + 58

Step 3: We consider the new divisor 70 and the new remainder 58, and apply the division lemma to get

70 = 58 x 1 + 12

We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get

58 = 12 x 4 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 268 and 338 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(268,70) = HCF(338,268) .

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

Step 1: Since 173 > 2, we apply the division lemma to 173 and 2, to get

173 = 2 x 86 + 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 173 is 1

Notice that 1 = HCF(2,1) = HCF(173,2) .

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Frequently Asked Questions on HCF of 268, 338, 173 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 268, 338, 173?

Answer: HCF of 268, 338, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 268, 338, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 268, 338, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.