Use our free GCF of Fractions Calculator tool to compute the GCF of 21/31, 756/39, 925/235 i.e 1/284115 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/31, 756/39, 925/235.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/31,756/39,925/235
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 21/31,756/39,925/235, numerators are 21,756,925
Denominators are 31,39,235
The GCF of 21,756,925 is 1 .
LCM of 31,39,235 is 284115.
The greatest common factor of 21/31,756/39,925/235 = [GCF of 21,756,925]/[LCM of 31,39,235]= 1/284115
Therefore, the GCF of 21/31,756/39,925/235 is 1/284115.
To find the highest common factor of 21,756,925, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The factors of 925 are 1, 5, 25, 37, 185, 925
The HCF of 21,756,925 is 1.
Lets's calculate GCF of 21,756,925
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Now, list down the factors of 925
:1,5,25,37,185,925
Greatest Common Factor
We found the factors 21,756,925 . The biggest common factor number is the GCF number.
So the greatest common factor 21,756,925 is 1.
Lets's calculate LCM of 31,39,235
Given numbers has no common factors except 1. So, there LCM is their product i.e 284115
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/284115
Therefore, the GCF of Fractions 21/31,756/39,925/235 is 1/284115
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 31,39,235 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,39,235) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,39,235) x common factors =1 x 1 = 1
LCM(31,39,235) = ( 31 × 39 × 235 ) / 1
LCM(31,39,235) = 284115 / 1
LCM(31,39,235) = 284115
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,756,925?
The HCF of 21,756,925 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 21/31, 756/39, 925/235?
Answer: GCF of Numerators as per given numbers 21/31, 756/39, 925/235 is
GCF of Numerators i.e. for 21,756,925 is 1
LCM of denominators i.e. for 31,39,235 is 284115.
Thus, GCF of Fractions is 1/284115.Finally, GCF of Fractions for 21/31, 756/39, 925/235 is 1/284115.