Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/40,80/16,23/51,730/35
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 45,80,23,730
Greatest Common Factor of Numerators i.e. GCF of 45,80,23,730 is 1 .
LCM of Denominators means LCM of 40,16,51,35 as per the given fractions.
LCM of 40,16,51,35 is 28560 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 45,80,23,730
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 730
List of positive integer factors of 730 that divides 730 without a remainder.
1,2,5,10,73,146,365,730
Greatest Common Factor
We found the factors 45,80,23,730 . The biggest common factor number is the GCF number.
So the greatest common factor 45,80,23,730 is 1.
Lets's calculate LCM of 40,16,51,35
2 | 40, 16, 51, 35 |
2 | 20, 8, 51, 35 |
2 | 10, 4, 51, 35 |
5 | 5, 2, 51, 35 |
1, 2, 51, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 2 x 51 x 7 = 28560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28560
Therefore, the GCF of Fractions 45/40,80/16,23/51,730/35 is 1/28560
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 40,16,51,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,16,51,35) = 1
common factors(in case of two or more numbers have common factors) = 40
GCF(40,16,51,35) x common factors =1 x 40 = 40
LCM(40,16,51,35) = ( 40 × 16 × 51 × 35 ) / 40
LCM(40,16,51,35) = 1142400 / 40
LCM(40,16,51,35) = 28560
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
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 45/40, 80/16, 23/51, 730/35?
Answer: GCF of Numerators as per given numbers 45/40, 80/16, 23/51, 730/35 is
GCF of Numerators i.e. for 45,80,23,730 is 1
LCM of denominators i.e. for 40,16,51,35 is 28560.
Thus, GCF of Fractions is 1/28560.Finally, GCF of Fractions for 45/40, 80/16, 23/51, 730/35 is 1/28560.