Highest Common Factor of 257, 230, 508 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 257, 230, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 257, 230, 508 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 257, 230, 508 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 257, 230, 508 is 1.

HCF(257, 230, 508) = 1

HCF of 257, 230, 508 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 257, 230, 508 is 1.

Highest Common Factor of 257,230,508 using Euclid's algorithm

Highest Common Factor of 257,230,508 is 1

Step 1: Since 257 > 230, we apply the division lemma to 257 and 230, to get

257 = 230 x 1 + 27

Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 27 and 230, to get

230 = 27 x 8 + 14

Step 3: We consider the new divisor 27 and the new remainder 14, and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 257 and 230 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(230,27) = HCF(257,230) .

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

Step 1: Since 508 > 1, we apply the division lemma to 508 and 1, to get

508 = 1 x 508 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 508 is 1

Notice that 1 = HCF(508,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 257, 230, 508 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 257, 230, 508?

Answer: HCF of 257, 230, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 257, 230, 508 using Euclid's Algorithm?

Answer: For arbitrary numbers 257, 230, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.