How to Find GCF of 78/458, 1274/1352?

GCF of 78/458, 1274/1352

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 78/458, 1274/1352 i.e 26/309608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/458, 1274/1352.

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 78/458,1274/1352?

Given fractions are 78/458,1274/1352

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 78/458,1274/1352, numerators are 78,1274

Denominators are 458,1352

The GCF of 78,1274 is 26 .

LCM of 458,1352 is 309608.

The greatest common factor of 78/458,1274/1352 = [GCF of 78,1274]/[LCM of 458,1352]= 26/309608

Therefore, the GCF of 78/458,1274/1352 is 26/309608.

Greatest Common Factor of 78,1274

To find the highest common factor of 78,1274, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 1274 are 1, 2, 7, 13, 14, 26, 49, 91, 98, 182, 637, 1274

The HCF of 78,1274 is 26.

Lets's calculate GCF of 78,1274

Greatest Common Factor (GCF) of 78,1274 By Common Division

2	78, 1274
13	39, 637
	3, 49

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 78,1274 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 1274

1,2,7,13,14,26,49,91,98,182,637,1274

Greatest Common Factor

We found the factors 78,1274 . The biggest common factor number is the GCF number.
So the greatest common factor 78,1274 is 26.

Lets's calculate LCM of 458,1352

Lowest Common Multiple of 458,1352 using Common Division

2	458, 1352
	229, 676

∴ So the LCM of the given numbers is 2 x 229 x 676 = 309608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/309608

Therefore, the GCF of Fractions 78/458,1274/1352 is 26/309608

Least Common Multiple of 458,1352 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 458,1352 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(458,1352) = 2

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

GCF(458,1352) x common factors =2 x 1 = 2

LCM(458,1352) = ( 458 × 1352 ) / 2

LCM(458,1352) = 619216 / 2

LCM(458,1352) = 309608

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 78/458, 1274/1352

1. What is the HCF of 78,1274?

The HCF of 78,1274 is 26

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 78/458, 1274/1352?

Answer: GCF of Numerators as per given numbers 78/458, 1274/1352 is

GCF of Numerators i.e. for 78,1274 is 26

LCM of denominators i.e. for 458,1352 is 309608.

Thus, GCF of Fractions is 26/309608.Finally, GCF of Fractions for 78/458, 1274/1352 is 26/309608.