Highest Common Factor of 664, 482, 405 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, 482, 405 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 664, 482, 405 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, 482, 405 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, 482, 405 is 1.

HCF(664, 482, 405) = 1

HCF of 664, 482, 405 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, 482, 405 is 1.

Highest Common Factor of 664,482,405 using Euclid's algorithm

Highest Common Factor of 664,482,405 is 1

Step 1: Since 664 > 482, we apply the division lemma to 664 and 482, to get

664 = 482 x 1 + 182

Step 2: Since the reminder 482 ≠ 0, we apply division lemma to 182 and 482, to get

482 = 182 x 2 + 118

Step 3: We consider the new divisor 182 and the new remainder 118, and apply the division lemma to get

182 = 118 x 1 + 64

We consider the new divisor 118 and the new remainder 64,and apply the division lemma to get

118 = 64 x 1 + 54

We consider the new divisor 64 and the new remainder 54,and apply the division lemma to get

64 = 54 x 1 + 10

We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get

54 = 10 x 5 + 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 664 and 482 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(64,54) = HCF(118,64) = HCF(182,118) = HCF(482,182) = HCF(664,482) .

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

Step 1: Since 405 > 2, we apply the division lemma to 405 and 2, to get

405 = 2 x 202 + 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 405 is 1

Notice that 1 = HCF(2,1) = HCF(405,2) .

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, 482, 405 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, 482, 405?

Answer: HCF of 664, 482, 405 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 664, 482, 405 using Euclid's Algorithm?

Answer: For arbitrary numbers 664, 482, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.