Highest Common Factor of 268, 691, 135 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, 691, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 268, 691, 135 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, 691, 135 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, 691, 135 is 1.

HCF(268, 691, 135) = 1

HCF of 268, 691, 135 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, 691, 135 is 1.

Highest Common Factor of 268,691,135 using Euclid's algorithm

Highest Common Factor of 268,691,135 is 1

Step 1: Since 691 > 268, we apply the division lemma to 691 and 268, to get

691 = 268 x 2 + 155

Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 155 and 268, to get

268 = 155 x 1 + 113

Step 3: We consider the new divisor 155 and the new remainder 113, and apply the division lemma to get

155 = 113 x 1 + 42

We consider the new divisor 113 and the new remainder 42,and apply the division lemma to get

113 = 42 x 2 + 29

We consider the new divisor 42 and the new remainder 29,and apply the division lemma to get

42 = 29 x 1 + 13

We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get

29 = 13 x 2 + 3

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

13 = 3 x 4 + 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 268 and 691 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(42,29) = HCF(113,42) = HCF(155,113) = HCF(268,155) = HCF(691,268) .

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

Step 1: Since 135 > 1, we apply the division lemma to 135 and 1, to get

135 = 1 x 135 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 135 is 1

Notice that 1 = HCF(135,1) .

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Frequently Asked Questions on HCF of 268, 691, 135 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, 691, 135?

Answer: HCF of 268, 691, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 268, 691, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 268, 691, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.