Highest Common Factor of 642, 877, 178 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 642, 877, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 877, 178 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 642, 877, 178 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 642, 877, 178 is 1.

HCF(642, 877, 178) = 1

HCF of 642, 877, 178 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 642, 877, 178 is 1.

Highest Common Factor of 642,877,178 using Euclid's algorithm

Highest Common Factor of 642,877,178 is 1

Step 1: Since 877 > 642, we apply the division lemma to 877 and 642, to get

877 = 642 x 1 + 235

Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 235 and 642, to get

642 = 235 x 2 + 172

Step 3: We consider the new divisor 235 and the new remainder 172, and apply the division lemma to get

235 = 172 x 1 + 63

We consider the new divisor 172 and the new remainder 63,and apply the division lemma to get

172 = 63 x 2 + 46

We consider the new divisor 63 and the new remainder 46,and apply the division lemma to get

63 = 46 x 1 + 17

We consider the new divisor 46 and the new remainder 17,and apply the division lemma to get

46 = 17 x 2 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 642 and 877 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(46,17) = HCF(63,46) = HCF(172,63) = HCF(235,172) = HCF(642,235) = HCF(877,642) .

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

Step 1: Since 178 > 1, we apply the division lemma to 178 and 1, to get

178 = 1 x 178 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 178 is 1

Notice that 1 = HCF(178,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 642, 877, 178 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 642, 877, 178?

Answer: HCF of 642, 877, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 877, 178 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 877, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.