Use our free GCF of Fractions Calculator tool to compute the GCF of 644/208, 735/977 i.e 7/203216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 644/208, 735/977.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 644/208,735/977
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 644/208,735/977, numerators are 644,735
Denominators are 208,977
The GCF of 644,735 is 7 .
LCM of 208,977 is 203216.
The greatest common factor of 644/208,735/977 = [GCF of 644,735]/[LCM of 208,977]= 7/203216
Therefore, the GCF of 644/208,735/977 is 7/203216.
To find the highest common factor of 644,735, we have to find the factors of both numbers and list the highest common factor.
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The HCF of 644,735 is 7.
Lets's calculate GCF of 644,735
7 | 644, 735 |
92, 105 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 644,735 . The biggest common factor number is the GCF number.
So the greatest common factor 644,735 is 7.
Lets's calculate LCM of 208,977
Given numbers has no common factors except 1. So, there LCM is their product i.e 203216
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/203216
Therefore, the GCF of Fractions 644/208,735/977 is 7/203216
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 208,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,977) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(208,977) x common factors =1 x 1 = 1
LCM(208,977) = ( 208 × 977 ) / 1
LCM(208,977) = 203216 / 1
LCM(208,977) = 203216
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 644,735?
The HCF of 644,735 is 7
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 644/208, 735/977?
Answer: GCF of Numerators as per given numbers 644/208, 735/977 is
GCF of Numerators i.e. for 644,735 is 7
LCM of denominators i.e. for 208,977 is 203216.
Thus, GCF of Fractions is 7/203216.Finally, GCF of Fractions for 644/208, 735/977 is 7/203216.