How to Find GCF of 1701/678, 3215/8120?

GCF of 1701/678, 3215/8120

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 1701/678, 3215/8120 i.e 1/2752680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1701/678, 3215/8120.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 1701/678,3215/8120?

Given fractions are 1701/678,3215/8120

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 1701/678,3215/8120, numerators are 1701,3215

Denominators are 678,8120

The GCF of 1701,3215 is 1 .

LCM of 678,8120 is 2752680.

The greatest common factor of 1701/678,3215/8120 = [GCF of 1701,3215]/[LCM of 678,8120]= 1/2752680

Therefore, the GCF of 1701/678,3215/8120 is 1/2752680.

Greatest Common Factor of 1701,3215

To find the highest common factor of 1701,3215, we have to find the factors of both numbers and list the highest common factor.

The factors of 1701 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 1701

The factors of 3215 are 1, 5, 643, 3215

The HCF of 1701,3215 is 1.

Lets's calculate GCF of 1701,3215

Greatest Common Factor (GCF) of 1701,3215 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 1701,3215 By Matching Biggest Common Factor Method

Now, list down the factors of 1701

1,3,7,9,21,27,63,81,189,243,567,1701

Now, list down the factors of 3215

1,5,643,3215

Greatest Common Factor

We found the factors 1701,3215 . The biggest common factor number is the GCF number.
So the greatest common factor 1701,3215 is 1.

Lets's calculate LCM of 678,8120

Lowest Common Multiple of 678,8120 using Common Division

2	678, 8120
	339, 4060

∴ So the LCM of the given numbers is 2 x 339 x 4060 = 2752680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2752680

Therefore, the GCF of Fractions 1701/678,3215/8120 is 1/2752680

Least Common Multiple of 678,8120 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 678,8120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(678,8120) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(678,8120) x common factors =2 x 1 = 2

LCM(678,8120) = ( 678 × 8120 ) / 2

LCM(678,8120) = 5505360 / 2

LCM(678,8120) = 2752680

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1701/678, 3215/8120

1. What is the HCF of 1701,3215?

The HCF of 1701,3215 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 1701/678, 3215/8120?

Answer: GCF of Numerators as per given numbers 1701/678, 3215/8120 is

GCF of Numerators i.e. for 1701,3215 is 1

LCM of denominators i.e. for 678,8120 is 2752680.

Thus, GCF of Fractions is 1/2752680.Finally, GCF of Fractions for 1701/678, 3215/8120 is 1/2752680.