Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/48,87/40,22/71,60/64
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 45,87,22,60
Greatest Common Factor of Numerators i.e. GCF of 45,87,22,60 is 1 .
LCM of Denominators means LCM of 48,40,71,64 as per the given fractions.
LCM of 48,40,71,64 is 68160 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 45,87,22,60
∴ 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 87
List of positive integer factors of 87 that divides 87 without a remainder.
1,3,29,87
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 45,87,22,60 . The biggest common factor number is the GCF number.
So the greatest common factor 45,87,22,60 is 1.
Lets's calculate LCM of 48,40,71,64
2 | 48, 40, 71, 64 |
2 | 24, 20, 71, 32 |
2 | 12, 10, 71, 16 |
2 | 6, 5, 71, 8 |
3, 5, 71, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 5 x 71 x 4 = 68160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68160
Therefore, the GCF of Fractions 45/48,87/40,22/71,60/64 is 1/68160
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 48,40,71,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,40,71,64) = 1
common factors(in case of two or more numbers have common factors) = 128
GCF(48,40,71,64) x common factors =1 x 128 = 128
LCM(48,40,71,64) = ( 48 × 40 × 71 × 64 ) / 128
LCM(48,40,71,64) = 8724480 / 128
LCM(48,40,71,64) = 68160
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 45/48, 87/40, 22/71, 60/64?
Answer: GCF of Numerators as per given numbers 45/48, 87/40, 22/71, 60/64 is
GCF of Numerators i.e. for 45,87,22,60 is 1
LCM of denominators i.e. for 48,40,71,64 is 68160.
Thus, GCF of Fractions is 1/68160.Finally, GCF of Fractions for 45/48, 87/40, 22/71, 60/64 is 1/68160.