Highest Common Factor of 8352, 3255, 91157 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 8352, 3255, 91157 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8352, 3255, 91157 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 8352, 3255, 91157 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 8352, 3255, 91157 is 1.

HCF(8352, 3255, 91157) = 1

HCF of 8352, 3255, 91157 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 8352, 3255, 91157 is 1.

Highest Common Factor of 8352,3255,91157 using Euclid's algorithm

Highest Common Factor of 8352,3255,91157 is 1

Step 1: Since 8352 > 3255, we apply the division lemma to 8352 and 3255, to get

8352 = 3255 x 2 + 1842

Step 2: Since the reminder 3255 ≠ 0, we apply division lemma to 1842 and 3255, to get

3255 = 1842 x 1 + 1413

Step 3: We consider the new divisor 1842 and the new remainder 1413, and apply the division lemma to get

1842 = 1413 x 1 + 429

We consider the new divisor 1413 and the new remainder 429,and apply the division lemma to get

1413 = 429 x 3 + 126

We consider the new divisor 429 and the new remainder 126,and apply the division lemma to get

429 = 126 x 3 + 51

We consider the new divisor 126 and the new remainder 51,and apply the division lemma to get

126 = 51 x 2 + 24

We consider the new divisor 51 and the new remainder 24,and apply the division lemma to get

51 = 24 x 2 + 3

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

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8352 and 3255 is 3

Notice that 3 = HCF(24,3) = HCF(51,24) = HCF(126,51) = HCF(429,126) = HCF(1413,429) = HCF(1842,1413) = HCF(3255,1842) = HCF(8352,3255) .

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

Step 1: Since 91157 > 3, we apply the division lemma to 91157 and 3, to get

91157 = 3 x 30385 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 91157 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(91157,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8352, 3255, 91157 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 8352, 3255, 91157?

Answer: HCF of 8352, 3255, 91157 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8352, 3255, 91157 using Euclid's Algorithm?

Answer: For arbitrary numbers 8352, 3255, 91157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.