Highest Common Factor of 8157, 3368, 82133 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 8157, 3368, 82133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8157, 3368, 82133 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 8157, 3368, 82133 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 8157, 3368, 82133 is 1.

HCF(8157, 3368, 82133) = 1

HCF of 8157, 3368, 82133 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 8157, 3368, 82133 is 1.

Highest Common Factor of 8157,3368,82133 using Euclid's algorithm

Highest Common Factor of 8157,3368,82133 is 1

Step 1: Since 8157 > 3368, we apply the division lemma to 8157 and 3368, to get

8157 = 3368 x 2 + 1421

Step 2: Since the reminder 3368 ≠ 0, we apply division lemma to 1421 and 3368, to get

3368 = 1421 x 2 + 526

Step 3: We consider the new divisor 1421 and the new remainder 526, and apply the division lemma to get

1421 = 526 x 2 + 369

We consider the new divisor 526 and the new remainder 369,and apply the division lemma to get

526 = 369 x 1 + 157

We consider the new divisor 369 and the new remainder 157,and apply the division lemma to get

369 = 157 x 2 + 55

We consider the new divisor 157 and the new remainder 55,and apply the division lemma to get

157 = 55 x 2 + 47

We consider the new divisor 55 and the new remainder 47,and apply the division lemma to get

55 = 47 x 1 + 8

We consider the new divisor 47 and the new remainder 8,and apply the division lemma to get

47 = 8 x 5 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8157 and 3368 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(47,8) = HCF(55,47) = HCF(157,55) = HCF(369,157) = HCF(526,369) = HCF(1421,526) = HCF(3368,1421) = HCF(8157,3368) .

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

Step 1: Since 82133 > 1, we apply the division lemma to 82133 and 1, to get

82133 = 1 x 82133 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 82133 is 1

Notice that 1 = HCF(82133,1) .

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Frequently Asked Questions on HCF of 8157, 3368, 82133 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 8157, 3368, 82133?

Answer: HCF of 8157, 3368, 82133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8157, 3368, 82133 using Euclid's Algorithm?

Answer: For arbitrary numbers 8157, 3368, 82133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.