Highest Common Factor of 1878, 6750, 75347 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 1878, 6750, 75347 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1878, 6750, 75347 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 1878, 6750, 75347 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 1878, 6750, 75347 is 1.

HCF(1878, 6750, 75347) = 1

HCF of 1878, 6750, 75347 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 1878, 6750, 75347 is 1.

Highest Common Factor of 1878,6750,75347 using Euclid's algorithm

Highest Common Factor of 1878,6750,75347 is 1

Step 1: Since 6750 > 1878, we apply the division lemma to 6750 and 1878, to get

6750 = 1878 x 3 + 1116

Step 2: Since the reminder 1878 ≠ 0, we apply division lemma to 1116 and 1878, to get

1878 = 1116 x 1 + 762

Step 3: We consider the new divisor 1116 and the new remainder 762, and apply the division lemma to get

1116 = 762 x 1 + 354

We consider the new divisor 762 and the new remainder 354,and apply the division lemma to get

762 = 354 x 2 + 54

We consider the new divisor 354 and the new remainder 54,and apply the division lemma to get

354 = 54 x 6 + 30

We consider the new divisor 54 and the new remainder 30,and apply the division lemma to get

54 = 30 x 1 + 24

We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get

30 = 24 x 1 + 6

We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1878 and 6750 is 6

Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(354,54) = HCF(762,354) = HCF(1116,762) = HCF(1878,1116) = HCF(6750,1878) .

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

Step 1: Since 75347 > 6, we apply the division lemma to 75347 and 6, to get

75347 = 6 x 12557 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 75347 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(75347,6) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 1878, 6750, 75347 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 1878, 6750, 75347?

Answer: HCF of 1878, 6750, 75347 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1878, 6750, 75347 using Euclid's Algorithm?

Answer: For arbitrary numbers 1878, 6750, 75347 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.