Use our free GCF of Fractions Calculator tool to compute the GCF of 265/257, 680/356 i.e 5/91492 easily. The following is the detailed procedure to determine the greatest common factor of fractions 265/257, 680/356.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 265/257,680/356
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 265/257,680/356, numerators are 265,680
Denominators are 257,356
The GCF of 265,680 is 5 .
LCM of 257,356 is 91492.
The greatest common factor of 265/257,680/356 = [GCF of 265,680]/[LCM of 257,356]= 5/91492
Therefore, the GCF of 265/257,680/356 is 5/91492.
To find the highest common factor of 265,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 265 are 1, 5, 53, 265
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 265,680 is 5.
Lets's calculate GCF of 265,680
5 | 265, 680 |
53, 136 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 265
:1,5,53,265
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 265,680 . The biggest common factor number is the GCF number.
So the greatest common factor 265,680 is 5.
Lets's calculate LCM of 257,356
Given numbers has no common factors except 1. So, there LCM is their product i.e 91492
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/91492
Therefore, the GCF of Fractions 265/257,680/356 is 5/91492
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 257,356 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(257,356) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(257,356) x common factors =1 x 1 = 1
LCM(257,356) = ( 257 × 356 ) / 1
LCM(257,356) = 91492 / 1
LCM(257,356) = 91492
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 265,680?
The HCF of 265,680 is 5
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 265/257, 680/356?
Answer: GCF of Numerators as per given numbers 265/257, 680/356 is
GCF of Numerators i.e. for 265,680 is 5
LCM of denominators i.e. for 257,356 is 91492.
Thus, GCF of Fractions is 5/91492.Finally, GCF of Fractions for 265/257, 680/356 is 5/91492.