How to Find GCF of 1254/584, 6327/7069?

GCF of 1254/584, 6327/7069

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 1254/584, 6327/7069 i.e 57/4128296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1254/584, 6327/7069.

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 1254/584,6327/7069?

Given fractions are 1254/584,6327/7069

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 1254/584,6327/7069, numerators are 1254,6327

Denominators are 584,7069

The GCF of 1254,6327 is 57 .

LCM of 584,7069 is 4128296.

The greatest common factor of 1254/584,6327/7069 = [GCF of 1254,6327]/[LCM of 584,7069]= 57/4128296

Therefore, the GCF of 1254/584,6327/7069 is 57/4128296.

Greatest Common Factor of 1254,6327

To find the highest common factor of 1254,6327, we have to find the factors of both numbers and list the highest common factor.

The factors of 1254 are 1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 66, 114, 209, 418, 627, 1254

The factors of 6327 are 1, 3, 9, 19, 37, 57, 111, 171, 333, 703, 2109, 6327

The HCF of 1254,6327 is 57.

Lets's calculate GCF of 1254,6327

Greatest Common Factor (GCF) of 1254,6327 By Common Division

3	1254, 6327
19	418, 2109
	22, 111

∴ So the GCF of the given numbers is 3 x 19 = 57

Greatest Common Factor of 1254,6327 By Matching Biggest Common Factor Method

Now, list down the factors of 1254

1,2,3,6,11,19,22,33,38,57,66,114,209,418,627,1254

Now, list down the factors of 6327

1,3,9,19,37,57,111,171,333,703,2109,6327

Greatest Common Factor

We found the factors 1254,6327 . The biggest common factor number is the GCF number.
So the greatest common factor 1254,6327 is 57.

Lets's calculate LCM of 584,7069

Lowest Common Multiple of 584,7069 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4128296

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/4128296

Therefore, the GCF of Fractions 1254/584,6327/7069 is 57/4128296

Least Common Multiple of 584,7069 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 584,7069 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(584,7069) = 1

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

GCF(584,7069) x common factors =1 x 1 = 1

LCM(584,7069) = ( 584 × 7069 ) / 1

LCM(584,7069) = 4128296 / 1

LCM(584,7069) = 4128296

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1254/584, 6327/7069

1. What is the HCF of 1254,6327?

The HCF of 1254,6327 is 57

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 1254/584, 6327/7069?

Answer: GCF of Numerators as per given numbers 1254/584, 6327/7069 is

GCF of Numerators i.e. for 1254,6327 is 57

LCM of denominators i.e. for 584,7069 is 4128296.

Thus, GCF of Fractions is 57/4128296.Finally, GCF of Fractions for 1254/584, 6327/7069 is 57/4128296.