Highest Common Factor of 45, 655, 204, 268 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 45, 655, 204, 268 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 45, 655, 204, 268 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 45, 655, 204, 268 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 45, 655, 204, 268 is 1.

HCF(45, 655, 204, 268) = 1

HCF of 45, 655, 204, 268 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 45, 655, 204, 268 is 1.

Highest Common Factor of 45,655,204,268 using Euclid's algorithm

Highest Common Factor of 45,655,204,268 is 1

Step 1: Since 655 > 45, we apply the division lemma to 655 and 45, to get

655 = 45 x 14 + 25

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 25 and 45, to get

45 = 25 x 1 + 20

Step 3: We consider the new divisor 25 and the new remainder 20, and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5, and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 45 and 655 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(655,45) .

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

Step 1: Since 204 > 5, we apply the division lemma to 204 and 5, to get

204 = 5 x 40 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma 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 5 and 204 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(204,5) .

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

Step 1: Since 268 > 1, we apply the division lemma to 268 and 1, to get

268 = 1 x 268 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 268 is 1

Notice that 1 = HCF(268,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 45, 655, 204, 268 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 45, 655, 204, 268?

Answer: HCF of 45, 655, 204, 268 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 45, 655, 204, 268 using Euclid's Algorithm?

Answer: For arbitrary numbers 45, 655, 204, 268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.