Highest Common Factor of 172, 135, 91 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 172, 135, 91 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 172, 135, 91 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 172, 135, 91 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 172, 135, 91 is 1.

HCF(172, 135, 91) = 1

HCF of 172, 135, 91 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 172, 135, 91 is 1.

Highest Common Factor of 172,135,91 using Euclid's algorithm

Highest Common Factor of 172,135,91 is 1

Step 1: Since 172 > 135, we apply the division lemma to 172 and 135, to get

172 = 135 x 1 + 37

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 37 and 135, to get

135 = 37 x 3 + 24

Step 3: We consider the new divisor 37 and the new remainder 24, and apply the division lemma to get

37 = 24 x 1 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 172 and 135 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(37,24) = HCF(135,37) = HCF(172,135) .

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

Step 1: Since 91 > 1, we apply the division lemma to 91 and 1, to get

91 = 1 x 91 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 91 is 1

Notice that 1 = HCF(91,1) .

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Frequently Asked Questions on HCF of 172, 135, 91 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 172, 135, 91?

Answer: HCF of 172, 135, 91 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 172, 135, 91 using Euclid's Algorithm?

Answer: For arbitrary numbers 172, 135, 91 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.