Use our free GCF of Fractions Calculator tool to compute the GCF of 34/65, 97/57, 77/80, 27/39 i.e 1/59280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/65, 97/57, 77/80, 27/39.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/65,97/57,77/80,27/39
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 34/65,97/57,77/80,27/39, numerators are 34,97,77,27
Denominators are 65,57,80,39
The GCF of 34,97,77,27 is 1 .
LCM of 65,57,80,39 is 59280.
The greatest common factor of 34/65,97/57,77/80,27/39 = [GCF of 34,97,77,27]/[LCM of 65,57,80,39]= 1/59280
Therefore, the GCF of 34/65,97/57,77/80,27/39 is 1/59280.
To find the highest common factor of 34,97,77,27, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 97 are 1, 97
The factors of 77 are 1, 7, 11, 77
The factors of 27 are 1, 3, 9, 27
The HCF of 34,97,77,27 is 1.
Lets's calculate GCF of 34,97,77,27
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 97
:1,97
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 27
:1,3,9,27
Greatest Common Factor
We found the factors 34,97,77,27 . The biggest common factor number is the GCF number.
So the greatest common factor 34,97,77,27 is 1.
Lets's calculate LCM of 65,57,80,39
3 | 65, 57, 80, 39 |
5 | 65, 19, 80, 13 |
13 | 13, 19, 16, 13 |
1, 19, 16, 1 |
∴ So the LCM of the given numbers is 3 x 5 x 13 x 1 x 19 x 16 x 1 = 59280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59280
Therefore, the GCF of Fractions 34/65,97/57,77/80,27/39 is 1/59280
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 65,57,80,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,57,80,39) = 1
common factors(in case of two or more numbers have common factors) = 195
GCF(65,57,80,39) x common factors =1 x 195 = 195
LCM(65,57,80,39) = ( 65 × 57 × 80 × 39 ) / 195
LCM(65,57,80,39) = 11559600 / 195
LCM(65,57,80,39) = 59280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 34,97,77,27?
The HCF of 34,97,77,27 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 34/65, 97/57, 77/80, 27/39?
Answer: GCF of Numerators as per given numbers 34/65, 97/57, 77/80, 27/39 is
GCF of Numerators i.e. for 34,97,77,27 is 1
LCM of denominators i.e. for 65,57,80,39 is 59280.
Thus, GCF of Fractions is 1/59280.Finally, GCF of Fractions for 34/65, 97/57, 77/80, 27/39 is 1/59280.