How to Find GCF of 54/345, 1278/6586?

GCF of 54/345, 1278/6586

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 54/345, 1278/6586 i.e 18/2272170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/345, 1278/6586.

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 54/345,1278/6586?

Given fractions are 54/345,1278/6586

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 54/345,1278/6586, numerators are 54,1278

Denominators are 345,6586

The GCF of 54,1278 is 18 .

LCM of 345,6586 is 2272170.

The greatest common factor of 54/345,1278/6586 = [GCF of 54,1278]/[LCM of 345,6586]= 18/2272170

Therefore, the GCF of 54/345,1278/6586 is 18/2272170.

Greatest Common Factor of 54,1278

To find the highest common factor of 54,1278, we have to find the factors of both numbers and list the highest common factor.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 1278 are 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278

The HCF of 54,1278 is 18.

Lets's calculate GCF of 54,1278

Greatest Common Factor (GCF) of 54,1278 By Common Division

2	54, 1278
3	27, 639
3	9, 213
	3, 71

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 54,1278 By Matching Biggest Common Factor Method

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 1278

1,2,3,6,9,18,71,142,213,426,639,1278

Greatest Common Factor

We found the factors 54,1278 . The biggest common factor number is the GCF number.
So the greatest common factor 54,1278 is 18.

Lets's calculate LCM of 345,6586

Lowest Common Multiple of 345,6586 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2272170

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/2272170

Therefore, the GCF of Fractions 54/345,1278/6586 is 18/2272170

Least Common Multiple of 345,6586 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 345,6586 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(345,6586) = 1

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

GCF(345,6586) x common factors =1 x 1 = 1

LCM(345,6586) = ( 345 × 6586 ) / 1

LCM(345,6586) = 2272170 / 1

LCM(345,6586) = 2272170

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FAQs on GCF of Fractions of 54/345, 1278/6586

1. What is the HCF of 54,1278?

The HCF of 54,1278 is 18

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 54/345, 1278/6586?

Answer: GCF of Numerators as per given numbers 54/345, 1278/6586 is

GCF of Numerators i.e. for 54,1278 is 18

LCM of denominators i.e. for 345,6586 is 2272170.

Thus, GCF of Fractions is 18/2272170.Finally, GCF of Fractions for 54/345, 1278/6586 is 18/2272170.