Highest Common Factor of 8514, 328 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 8514, 328 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8514, 328 is 2 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 8514, 328 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 8514, 328 is 2.

HCF(8514, 328) = 2

HCF of 8514, 328 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 8514, 328 is 2.

Highest Common Factor of 8514,328 using Euclid's algorithm

Highest Common Factor of 8514,328 is 2

Step 1: Since 8514 > 328, we apply the division lemma to 8514 and 328, to get

8514 = 328 x 25 + 314

Step 2: Since the reminder 328 ≠ 0, we apply division lemma to 314 and 328, to get

328 = 314 x 1 + 14

Step 3: We consider the new divisor 314 and the new remainder 14, and apply the division lemma to get

314 = 14 x 22 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8514 and 328 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(314,14) = HCF(328,314) = HCF(8514,328) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8514, 328 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 8514, 328?

Answer: HCF of 8514, 328 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8514, 328 using Euclid's Algorithm?

Answer: For arbitrary numbers 8514, 328 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.