Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/68,44/40,64/56,31/765
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 34,44,64,31
Greatest Common Factor of Numerators i.e. GCF of 34,44,64,31 is 1 .
LCM of Denominators means LCM of 68,40,56,765 as per the given fractions.
LCM of 68,40,56,765 is 42840 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 34,44,64,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
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 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Greatest Common Factor
We found the factors 34,44,64,31 . The biggest common factor number is the GCF number.
So the greatest common factor 34,44,64,31 is 1.
Lets's calculate LCM of 68,40,56,765
2 | 68, 40, 56, 765 |
2 | 34, 20, 28, 765 |
2 | 17, 10, 14, 765 |
5 | 17, 5, 7, 765 |
17 | 17, 1, 7, 153 |
1, 1, 7, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 17 x 1 x 1 x 7 x 9 = 42840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42840
Therefore, the GCF of Fractions 34/68,44/40,64/56,31/765 is 1/42840
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 68,40,56,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,40,56,765) = 1
common factors(in case of two or more numbers have common factors) = 2720
GCF(68,40,56,765) x common factors =1 x 2720 = 2720
LCM(68,40,56,765) = ( 68 × 40 × 56 × 765 ) / 2720
LCM(68,40,56,765) = 116524800 / 2720
LCM(68,40,56,765) = 42840
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 34/68, 44/40, 64/56, 31/765?
Answer: GCF of Numerators as per given numbers 34/68, 44/40, 64/56, 31/765 is
GCF of Numerators i.e. for 34,44,64,31 is 1
LCM of denominators i.e. for 68,40,56,765 is 42840.
Thus, GCF of Fractions is 1/42840.Finally, GCF of Fractions for 34/68, 44/40, 64/56, 31/765 is 1/42840.