Highest Common Factor of 808, 500, 529 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 808, 500, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 808, 500, 529 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 808, 500, 529 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 808, 500, 529 is 1.

HCF(808, 500, 529) = 1

HCF of 808, 500, 529 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 808, 500, 529 is 1.

Highest Common Factor of 808,500,529 using Euclid's algorithm

Highest Common Factor of 808,500,529 is 1

Step 1: Since 808 > 500, we apply the division lemma to 808 and 500, to get

808 = 500 x 1 + 308

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 308 and 500, to get

500 = 308 x 1 + 192

Step 3: We consider the new divisor 308 and the new remainder 192, and apply the division lemma to get

308 = 192 x 1 + 116

We consider the new divisor 192 and the new remainder 116,and apply the division lemma to get

192 = 116 x 1 + 76

We consider the new divisor 116 and the new remainder 76,and apply the division lemma to get

116 = 76 x 1 + 40

We consider the new divisor 76 and the new remainder 40,and apply the division lemma to get

76 = 40 x 1 + 36

We consider the new divisor 40 and the new remainder 36,and apply the division lemma to get

40 = 36 x 1 + 4

We consider the new divisor 36 and the new remainder 4,and apply the division lemma to get

36 = 4 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 808 and 500 is 4

Notice that 4 = HCF(36,4) = HCF(40,36) = HCF(76,40) = HCF(116,76) = HCF(192,116) = HCF(308,192) = HCF(500,308) = HCF(808,500) .

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

Step 1: Since 529 > 4, we apply the division lemma to 529 and 4, to get

529 = 4 x 132 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 529 is 1

Notice that 1 = HCF(4,1) = HCF(529,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 808, 500, 529 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 808, 500, 529?

Answer: HCF of 808, 500, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 808, 500, 529 using Euclid's Algorithm?

Answer: For arbitrary numbers 808, 500, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.