Highest Common Factor of 527, 874 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 527, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 527, 874 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 527, 874 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 527, 874 is 1.

HCF(527, 874) = 1

HCF of 527, 874 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 527, 874 is 1.

Highest Common Factor of 527,874 using Euclid's algorithm

Highest Common Factor of 527,874 is 1

Step 1: Since 874 > 527, we apply the division lemma to 874 and 527, to get

874 = 527 x 1 + 347

Step 2: Since the reminder 527 ≠ 0, we apply division lemma to 347 and 527, to get

527 = 347 x 1 + 180

Step 3: We consider the new divisor 347 and the new remainder 180, and apply the division lemma to get

347 = 180 x 1 + 167

We consider the new divisor 180 and the new remainder 167,and apply the division lemma to get

180 = 167 x 1 + 13

We consider the new divisor 167 and the new remainder 13,and apply the division lemma to get

167 = 13 x 12 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 527 and 874 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(167,13) = HCF(180,167) = HCF(347,180) = HCF(527,347) = HCF(874,527) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 527, 874 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 527, 874?

Answer: HCF of 527, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 527, 874 using Euclid's Algorithm?

Answer: For arbitrary numbers 527, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.