Highest Common Factor of 176, 629, 869 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 176, 629, 869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 176, 629, 869 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 176, 629, 869 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 176, 629, 869 is 1.

HCF(176, 629, 869) = 1

HCF of 176, 629, 869 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 176, 629, 869 is 1.

Highest Common Factor of 176,629,869 using Euclid's algorithm

Highest Common Factor of 176,629,869 is 1

Step 1: Since 629 > 176, we apply the division lemma to 629 and 176, to get

629 = 176 x 3 + 101

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 101 and 176, to get

176 = 101 x 1 + 75

Step 3: We consider the new divisor 101 and the new remainder 75, and apply the division lemma to get

101 = 75 x 1 + 26

We consider the new divisor 75 and the new remainder 26,and apply the division lemma to get

75 = 26 x 2 + 23

We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get

26 = 23 x 1 + 3

We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get

23 = 3 x 7 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 176 and 629 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(75,26) = HCF(101,75) = HCF(176,101) = HCF(629,176) .

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

Step 1: Since 869 > 1, we apply the division lemma to 869 and 1, to get

869 = 1 x 869 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 869 is 1

Notice that 1 = HCF(869,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 176, 629, 869 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 176, 629, 869?

Answer: HCF of 176, 629, 869 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 176, 629, 869 using Euclid's Algorithm?

Answer: For arbitrary numbers 176, 629, 869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.