Use our free GCF of Fractions Calculator tool to compute the GCF of 268/102, 749/135 i.e 1/4590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 268/102, 749/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 268/102,749/135
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 268/102,749/135, numerators are 268,749
Denominators are 102,135
The GCF of 268,749 is 1 .
LCM of 102,135 is 4590.
The greatest common factor of 268/102,749/135 = [GCF of 268,749]/[LCM of 102,135]= 1/4590
Therefore, the GCF of 268/102,749/135 is 1/4590.
To find the highest common factor of 268,749, we have to find the factors of both numbers and list the highest common factor.
The factors of 268 are 1, 2, 4, 67, 134, 268
The factors of 749 are 1, 7, 107, 749
The HCF of 268,749 is 1.
Lets's calculate GCF of 268,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 268
:1,2,4,67,134,268
Now, list down the factors of 749
:1,7,107,749
Greatest Common Factor
We found the factors 268,749 . The biggest common factor number is the GCF number.
So the greatest common factor 268,749 is 1.
Lets's calculate LCM of 102,135
3 | 102, 135 |
34, 45 |
∴ So the LCM of the given numbers is 3 x 34 x 45 = 4590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4590
Therefore, the GCF of Fractions 268/102,749/135 is 1/4590
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 102,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,135) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(102,135) x common factors =3 x 1 = 3
LCM(102,135) = ( 102 × 135 ) / 3
LCM(102,135) = 13770 / 3
LCM(102,135) = 4590
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 268,749?
The HCF of 268,749 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 268/102, 749/135?
Answer: GCF of Numerators as per given numbers 268/102, 749/135 is
GCF of Numerators i.e. for 268,749 is 1
LCM of denominators i.e. for 102,135 is 4590.
Thus, GCF of Fractions is 1/4590.Finally, GCF of Fractions for 268/102, 749/135 is 1/4590.