Highest Common Factor of 538, 824, 457 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 538, 824, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 538, 824, 457 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 538, 824, 457 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 538, 824, 457 is 1.

HCF(538, 824, 457) = 1

HCF of 538, 824, 457 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 538, 824, 457 is 1.

Highest Common Factor of 538,824,457 using Euclid's algorithm

Highest Common Factor of 538,824,457 is 1

Step 1: Since 824 > 538, we apply the division lemma to 824 and 538, to get

824 = 538 x 1 + 286

Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 286 and 538, to get

538 = 286 x 1 + 252

Step 3: We consider the new divisor 286 and the new remainder 252, and apply the division lemma to get

286 = 252 x 1 + 34

We consider the new divisor 252 and the new remainder 34,and apply the division lemma to get

252 = 34 x 7 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 538 and 824 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(252,34) = HCF(286,252) = HCF(538,286) = HCF(824,538) .

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

Step 1: Since 457 > 2, we apply the division lemma to 457 and 2, to get

457 = 2 x 228 + 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 457 is 1

Notice that 1 = HCF(2,1) = HCF(457,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 538, 824, 457 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 538, 824, 457?

Answer: HCF of 538, 824, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 538, 824, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 538, 824, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.