Use our free GCF of Fractions Calculator tool to compute the GCF of 262/548, 205/144 i.e 1/19728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 262/548, 205/144.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 262/548,205/144
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 262/548,205/144, numerators are 262,205
Denominators are 548,144
The GCF of 262,205 is 1 .
LCM of 548,144 is 19728.
The greatest common factor of 262/548,205/144 = [GCF of 262,205]/[LCM of 548,144]= 1/19728
Therefore, the GCF of 262/548,205/144 is 1/19728.
To find the highest common factor of 262,205, we have to find the factors of both numbers and list the highest common factor.
The factors of 262 are 1, 2, 131, 262
The factors of 205 are 1, 5, 41, 205
The HCF of 262,205 is 1.
Lets's calculate GCF of 262,205
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 262
:1,2,131,262
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 262,205 . The biggest common factor number is the GCF number.
So the greatest common factor 262,205 is 1.
Lets's calculate LCM of 548,144
2 | 548, 144 |
2 | 274, 72 |
137, 36 |
∴ So the LCM of the given numbers is 2 x 2 x 137 x 36 = 19728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19728
Therefore, the GCF of Fractions 262/548,205/144 is 1/19728
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 548,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(548,144) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(548,144) x common factors =4 x 1 = 4
LCM(548,144) = ( 548 × 144 ) / 4
LCM(548,144) = 78912 / 4
LCM(548,144) = 19728
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 262,205?
The HCF of 262,205 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 262/548, 205/144?
Answer: GCF of Numerators as per given numbers 262/548, 205/144 is
GCF of Numerators i.e. for 262,205 is 1
LCM of denominators i.e. for 548,144 is 19728.
Thus, GCF of Fractions is 1/19728.Finally, GCF of Fractions for 262/548, 205/144 is 1/19728.