Greatest Common Factor of 61/24, 78/45, 85/40, 975/10

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 61/24, 78/45, 85/40, 975/10

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 61/24,78/45,85/40,975/10

Given fractions are 61/24,78/45,85/40,975/10

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 61,78,85,975

Greatest Common Factor of Numerators i.e. GCF of 61,78,85,975 is 1 .

LCM of Denominators means LCM of 24,45,40,10 as per the given fractions.

LCM of 24,45,40,10 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 61,78,85,975

GCF of Fractions 61/24,78/45,85/40,975/10 is 1/360

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 61,78,85,975 By Matching Biggest Common Factor Method

Greatest Common Factor of 61,78,85,975 By Matching Biggest Common Factor Method

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

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

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Factors of 975

List of positive integer factors of 975 that divides 975 without a remainder.

1,3,5,13,15,25,39,65,75,195,325,975

Greatest Common Factor

We found the factors 61,78,85,975 . The biggest common factor number is the GCF number.
So the greatest common factor 61,78,85,975 is 1.

Lets's calculate LCM of 24,45,40,10

2 24, 45, 40, 10
2 12, 45, 20, 5
2 6, 45, 10, 5
3 3, 45, 5, 5
5 1, 15, 5, 5
1, 3, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 3 x 1 x 1 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360

Therefore, the GCF of Fractions 61/24,78/45,85/40,975/10 is 1/360

Least Common Multiple of 24,45,40,10 with GCF Formula

Least Common Multiple of 24,45,40,10 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 24,45,40,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(24,45,40,10) = 1

common factors(in case of two or more numbers have common factors) = 1200

GCF(24,45,40,10) x common factors =1 x 1200 = 1200

LCM(24,45,40,10) = ( 24 × 45 × 40 × 10 ) / 1200

LCM(24,45,40,10) = 432000 / 1200

LCM(24,45,40,10) = 360


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 61/24, 78/45, 85/40, 975/10

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 61/24, 78/45, 85/40, 975/10?

Answer: GCF of Numerators as per given numbers 61/24, 78/45, 85/40, 975/10 is

GCF of Numerators i.e. for 61,78,85,975 is 1

LCM of denominators i.e. for 24,45,40,10 is 360.

Thus, GCF of Fractions is 1/360.Finally, GCF of Fractions for 61/24, 78/45, 85/40, 975/10 is 1/360.