Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/45,66/94,80/18,55/435
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 75,66,80,55
Greatest Common Factor of Numerators i.e. GCF of 75,66,80,55 is 1 .
LCM of Denominators means LCM of 45,94,18,435 as per the given fractions.
LCM of 45,94,18,435 is 122670 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,66,80,55
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
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 55
List of positive integer factors of 55 that divides 55 without a remainder.
1,5,11,55
Greatest Common Factor
We found the factors 75,66,80,55 . The biggest common factor number is the GCF number.
So the greatest common factor 75,66,80,55 is 1.
Lets's calculate LCM of 45,94,18,435
2 | 45, 94, 18, 435 |
3 | 45, 47, 9, 435 |
3 | 15, 47, 3, 145 |
5 | 5, 47, 1, 145 |
1, 47, 1, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 47 x 1 x 29 = 122670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122670
Therefore, the GCF of Fractions 75/45,66/94,80/18,55/435 is 1/122670
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 45,94,18,435 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,94,18,435) = 1
common factors(in case of two or more numbers have common factors) = 270
GCF(45,94,18,435) x common factors =1 x 270 = 270
LCM(45,94,18,435) = ( 45 × 94 × 18 × 435 ) / 270
LCM(45,94,18,435) = 33120900 / 270
LCM(45,94,18,435) = 122670
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 75/45, 66/94, 80/18, 55/435?
Answer: GCF of Numerators as per given numbers 75/45, 66/94, 80/18, 55/435 is
GCF of Numerators i.e. for 75,66,80,55 is 1
LCM of denominators i.e. for 45,94,18,435 is 122670.
Thus, GCF of Fractions is 1/122670.Finally, GCF of Fractions for 75/45, 66/94, 80/18, 55/435 is 1/122670.