How to Find GCF of 786/258, 470/504?

GCF of 786/258, 470/504

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 786/258, 470/504 i.e 2/21672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 786/258, 470/504.

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 786/258,470/504?

Given fractions are 786/258,470/504

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 786/258,470/504, numerators are 786,470

Denominators are 258,504

The GCF of 786,470 is 2 .

LCM of 258,504 is 21672.

The greatest common factor of 786/258,470/504 = [GCF of 786,470]/[LCM of 258,504]= 2/21672

Therefore, the GCF of 786/258,470/504 is 2/21672.

Greatest Common Factor of 786,470

To find the highest common factor of 786,470, we have to find the factors of both numbers and list the highest common factor.

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786

The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470

The HCF of 786,470 is 2.

Lets's calculate GCF of 786,470

Greatest Common Factor (GCF) of 786,470 By Common Division

2	786, 470
	393, 235

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 786,470 By Matching Biggest Common Factor Method

Now, list down the factors of 786

1,2,3,6,131,262,393,786

Now, list down the factors of 470

1,2,5,10,47,94,235,470

Greatest Common Factor

We found the factors 786,470 . The biggest common factor number is the GCF number.
So the greatest common factor 786,470 is 2.

Lets's calculate LCM of 258,504

Lowest Common Multiple of 258,504 using Common Division

2	258, 504
3	129, 252
	43, 84

∴ So the LCM of the given numbers is 2 x 3 x 43 x 84 = 21672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21672

Therefore, the GCF of Fractions 786/258,470/504 is 2/21672

Least Common Multiple of 258,504 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 258,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(258,504) = 6

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

GCF(258,504) x common factors =6 x 1 = 6

LCM(258,504) = ( 258 × 504 ) / 6

LCM(258,504) = 130032 / 6

LCM(258,504) = 21672

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 786/258, 470/504

1. What is the HCF of 786,470?

The HCF of 786,470 is 2

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 786/258, 470/504?

Answer: GCF of Numerators as per given numbers 786/258, 470/504 is

GCF of Numerators i.e. for 786,470 is 2

LCM of denominators i.e. for 258,504 is 21672.

Thus, GCF of Fractions is 2/21672.Finally, GCF of Fractions for 786/258, 470/504 is 2/21672.