Greatest Common Factor of 735/509, 5782/105

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 735/509, 5782/105

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 735/509,5782/105

Given fractions are 735/509,5782/105

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 735,5782

Greatest Common Factor of Numerators i.e. GCF of 735,5782 is 49 .

LCM of Denominators means LCM of 509,105 as per the given fractions.

LCM of 509,105 is 53445 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 735,5782

GCF of Fractions 735/509,5782/105 is 49/53445

7 735, 5782
7 105, 826
15, 118

∴ So the GCF of the given numbers is 7 x 7 = 49

Greatest Common Factor of 735,5782 By Matching Biggest Common Factor Method

Greatest Common Factor of 735,5782 By Matching Biggest Common Factor Method

Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1,3,5,7,15,21,35,49,105,147,245,735

Factors of 5782

List of positive integer factors of 5782 that divides 5782 without a remainder.

1,2,7,14,49,59,98,118,413,826,2891,5782

Greatest Common Factor

We found the factors 735,5782 . The biggest common factor number is the GCF number.
So the greatest common factor 735,5782 is 49.

Lets's calculate LCM of 509,105

Given numbers has no common factors except 1. So, there LCM is their product i.e 53445

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 49/53445

Therefore, the GCF of Fractions 735/509,5782/105 is 49/53445

Least Common Multiple of 509,105 with GCF Formula

Least Common Multiple of 509,105 with GCF Formula

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

We need to calculate greatest common factor of 509,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(509,105) = 1

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

GCF(509,105) x common factors =1 x 1 = 1

LCM(509,105) = ( 509 × 105 ) / 1

LCM(509,105) = 53445 / 1

LCM(509,105) = 53445


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 735/509, 5782/105

1. 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.

2. What is the GCF of Fractions for 735/509, 5782/105?

Answer: GCF of Numerators as per given numbers 735/509, 5782/105 is

GCF of Numerators i.e. for 735,5782 is 49

LCM of denominators i.e. for 509,105 is 53445.

Thus, GCF of Fractions is 49/53445.Finally, GCF of Fractions for 735/509, 5782/105 is 49/53445.