Highest Common Factor of 874, 659 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 874, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 659 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 874, 659 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 874, 659 is 1.

HCF(874, 659) = 1

HCF of 874, 659 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 874, 659 is 1.

Highest Common Factor of 874,659 using Euclid's algorithm

Highest Common Factor of 874,659 is 1

Step 1: Since 874 > 659, we apply the division lemma to 874 and 659, to get

874 = 659 x 1 + 215

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 215 and 659, to get

659 = 215 x 3 + 14

Step 3: We consider the new divisor 215 and the new remainder 14, and apply the division lemma to get

215 = 14 x 15 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 874 and 659 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(215,14) = HCF(659,215) = HCF(874,659) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 874, 659 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 874, 659?

Answer: HCF of 874, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.