Use our free GCF of Fractions Calculator tool to compute the GCF of 278/596, 278/500 i.e 278/74500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/596, 278/500.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 278/596,278/500
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 278/596,278/500, numerators are 278,278
Denominators are 596,500
The GCF of 278,278 is 278 .
LCM of 596,500 is 74500.
The greatest common factor of 278/596,278/500 = [GCF of 278,278]/[LCM of 596,500]= 278/74500
Therefore, the GCF of 278/596,278/500 is 278/74500.
To find the highest common factor of 278,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 278 are 1, 2, 139, 278
The HCF of 278,278 is 278.
Lets's calculate GCF of 278,278
2 | 278, 278 |
139 | 139, 139 |
1, 1 |
∴ So the GCF of the given numbers is 2 x 139 = 278
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 278,278 . The biggest common factor number is the GCF number.
So the greatest common factor 278,278 is 278.
Lets's calculate LCM of 596,500
2 | 596, 500 |
2 | 298, 250 |
149, 125 |
∴ So the LCM of the given numbers is 2 x 2 x 149 x 125 = 74500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 278/74500
Therefore, the GCF of Fractions 278/596,278/500 is 278/74500
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 596,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(596,500) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(596,500) x common factors =4 x 1 = 4
LCM(596,500) = ( 596 × 500 ) / 4
LCM(596,500) = 298000 / 4
LCM(596,500) = 74500
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 278,278?
The HCF of 278,278 is 278
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 278/596, 278/500?
Answer: GCF of Numerators as per given numbers 278/596, 278/500 is
GCF of Numerators i.e. for 278,278 is 278
LCM of denominators i.e. for 596,500 is 74500.
Thus, GCF of Fractions is 278/74500.Finally, GCF of Fractions for 278/596, 278/500 is 278/74500.