Highest Common Factor of 324, 928, 321 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 324, 928, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 324, 928, 321 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 324, 928, 321 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 324, 928, 321 is 1.

HCF(324, 928, 321) = 1

HCF of 324, 928, 321 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 324, 928, 321 is 1.

Highest Common Factor of 324,928,321 using Euclid's algorithm

Highest Common Factor of 324,928,321 is 1

Step 1: Since 928 > 324, we apply the division lemma to 928 and 324, to get

928 = 324 x 2 + 280

Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 280 and 324, to get

324 = 280 x 1 + 44

Step 3: We consider the new divisor 280 and the new remainder 44, and apply the division lemma to get

280 = 44 x 6 + 16

We consider the new divisor 44 and the new remainder 16,and apply the division lemma to get

44 = 16 x 2 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 324 and 928 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(44,16) = HCF(280,44) = HCF(324,280) = HCF(928,324) .

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

Step 1: Since 321 > 4, we apply the division lemma to 321 and 4, to get

321 = 4 x 80 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 321 is 1

Notice that 1 = HCF(4,1) = HCF(321,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 324, 928, 321 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 324, 928, 321?

Answer: HCF of 324, 928, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 324, 928, 321 using Euclid's Algorithm?

Answer: For arbitrary numbers 324, 928, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.