Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/57,37/83,34/32,640/64
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 64,37,34,640
Greatest Common Factor of Numerators i.e. GCF of 64,37,34,640 is 1 .
LCM of Denominators means LCM of 57,83,32,64 as per the given fractions.
LCM of 57,83,32,64 is 302784 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 64,37,34,640
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
Factors of 37
List of positive integer factors of 37 that divides 37 without a remainder.
1,37
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 640
List of positive integer factors of 640 that divides 640 without a remainder.
1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Greatest Common Factor
We found the factors 64,37,34,640 . The biggest common factor number is the GCF number.
So the greatest common factor 64,37,34,640 is 1.
Lets's calculate LCM of 57,83,32,64
2 | 57, 83, 32, 64 |
2 | 57, 83, 16, 32 |
2 | 57, 83, 8, 16 |
2 | 57, 83, 4, 8 |
2 | 57, 83, 2, 4 |
57, 83, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 57 x 83 x 1 x 2 = 302784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/302784
Therefore, the GCF of Fractions 64/57,37/83,34/32,640/64 is 1/302784
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 57,83,32,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,83,32,64) = 1
common factors(in case of two or more numbers have common factors) = 32
GCF(57,83,32,64) x common factors =1 x 32 = 32
LCM(57,83,32,64) = ( 57 × 83 × 32 × 64 ) / 32
LCM(57,83,32,64) = 9689088 / 32
LCM(57,83,32,64) = 302784
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 64/57, 37/83, 34/32, 640/64?
Answer: GCF of Numerators as per given numbers 64/57, 37/83, 34/32, 640/64 is
GCF of Numerators i.e. for 64,37,34,640 is 1
LCM of denominators i.e. for 57,83,32,64 is 302784.
Thus, GCF of Fractions is 1/302784.Finally, GCF of Fractions for 64/57, 37/83, 34/32, 640/64 is 1/302784.