Highest Common Factor of 132, 215, 193 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 132, 215, 193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 132, 215, 193 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 132, 215, 193 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 132, 215, 193 is 1.

HCF(132, 215, 193) = 1

HCF of 132, 215, 193 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 132, 215, 193 is 1.

Highest Common Factor of 132,215,193 using Euclid's algorithm

Highest Common Factor of 132,215,193 is 1

Step 1: Since 215 > 132, we apply the division lemma to 215 and 132, to get

215 = 132 x 1 + 83

Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 83 and 132, to get

132 = 83 x 1 + 49

Step 3: We consider the new divisor 83 and the new remainder 49, and apply the division lemma to get

83 = 49 x 1 + 34

We consider the new divisor 49 and the new remainder 34,and apply the division lemma to get

49 = 34 x 1 + 15

We consider the new divisor 34 and the new remainder 15,and apply the division lemma to get

34 = 15 x 2 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 132 and 215 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(34,15) = HCF(49,34) = HCF(83,49) = HCF(132,83) = HCF(215,132) .

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

Step 1: Since 193 > 1, we apply the division lemma to 193 and 1, to get

193 = 1 x 193 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 193 is 1

Notice that 1 = HCF(193,1) .

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Frequently Asked Questions on HCF of 132, 215, 193 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 132, 215, 193?

Answer: HCF of 132, 215, 193 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 132, 215, 193 using Euclid's Algorithm?

Answer: For arbitrary numbers 132, 215, 193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.