Highest Common Factor of 508, 714, 281 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 508, 714, 281 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 714, 281 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 508, 714, 281 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 508, 714, 281 is 1.

HCF(508, 714, 281) = 1

HCF of 508, 714, 281 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 508, 714, 281 is 1.

Highest Common Factor of 508,714,281 using Euclid's algorithm

Highest Common Factor of 508,714,281 is 1

Step 1: Since 714 > 508, we apply the division lemma to 714 and 508, to get

714 = 508 x 1 + 206

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 206 and 508, to get

508 = 206 x 2 + 96

Step 3: We consider the new divisor 206 and the new remainder 96, and apply the division lemma to get

206 = 96 x 2 + 14

We consider the new divisor 96 and the new remainder 14,and apply the division lemma to get

96 = 14 x 6 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 508 and 714 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(96,14) = HCF(206,96) = HCF(508,206) = HCF(714,508) .

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

Step 1: Since 281 > 2, we apply the division lemma to 281 and 2, to get

281 = 2 x 140 + 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 281 is 1

Notice that 1 = HCF(2,1) = HCF(281,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 508, 714, 281 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 508, 714, 281?

Answer: HCF of 508, 714, 281 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 714, 281 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 714, 281 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.