Highest Common Factor of 500, 966, 329 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 500, 966, 329 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 500, 966, 329 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 500, 966, 329 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 500, 966, 329 is 1.

HCF(500, 966, 329) = 1

HCF of 500, 966, 329 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 500, 966, 329 is 1.

Highest Common Factor of 500,966,329 using Euclid's algorithm

Highest Common Factor of 500,966,329 is 1

Step 1: Since 966 > 500, we apply the division lemma to 966 and 500, to get

966 = 500 x 1 + 466

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 466 and 500, to get

500 = 466 x 1 + 34

Step 3: We consider the new divisor 466 and the new remainder 34, and apply the division lemma to get

466 = 34 x 13 + 24

We consider the new divisor 34 and the new remainder 24,and apply the division lemma to get

34 = 24 x 1 + 10

We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get

24 = 10 x 2 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 500 and 966 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(466,34) = HCF(500,466) = HCF(966,500) .

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

Step 1: Since 329 > 2, we apply the division lemma to 329 and 2, to get

329 = 2 x 164 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 329 is 1

Notice that 1 = HCF(2,1) = HCF(329,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 500, 966, 329 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 500, 966, 329?

Answer: HCF of 500, 966, 329 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 500, 966, 329 using Euclid's Algorithm?

Answer: For arbitrary numbers 500, 966, 329 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.