Highest Common Factor of 664, 910, 323 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 664, 910, 323 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 664, 910, 323 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 664, 910, 323 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 664, 910, 323 is 1.

HCF(664, 910, 323) = 1

HCF of 664, 910, 323 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 664, 910, 323 is 1.

Highest Common Factor of 664,910,323 using Euclid's algorithm

Highest Common Factor of 664,910,323 is 1

Step 1: Since 910 > 664, we apply the division lemma to 910 and 664, to get

910 = 664 x 1 + 246

Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 246 and 664, to get

664 = 246 x 2 + 172

Step 3: We consider the new divisor 246 and the new remainder 172, and apply the division lemma to get

246 = 172 x 1 + 74

We consider the new divisor 172 and the new remainder 74,and apply the division lemma to get

172 = 74 x 2 + 24

We consider the new divisor 74 and the new remainder 24,and apply the division lemma to get

74 = 24 x 3 + 2

We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 664 and 910 is 2

Notice that 2 = HCF(24,2) = HCF(74,24) = HCF(172,74) = HCF(246,172) = HCF(664,246) = HCF(910,664) .

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

Step 1: Since 323 > 2, we apply the division lemma to 323 and 2, to get

323 = 2 x 161 + 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 323 is 1

Notice that 1 = HCF(2,1) = HCF(323,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 664, 910, 323 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 664, 910, 323?

Answer: HCF of 664, 910, 323 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 664, 910, 323 using Euclid's Algorithm?

Answer: For arbitrary numbers 664, 910, 323 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.