Use our free GCF of Fractions Calculator tool to compute the GCF of 657/540, 769/360 i.e 1/1080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/540, 769/360.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 657/540,769/360
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 657/540,769/360, numerators are 657,769
Denominators are 540,360
The GCF of 657,769 is 1 .
LCM of 540,360 is 1080.
The greatest common factor of 657/540,769/360 = [GCF of 657,769]/[LCM of 540,360]= 1/1080
Therefore, the GCF of 657/540,769/360 is 1/1080.
To find the highest common factor of 657,769, we have to find the factors of both numbers and list the highest common factor.
The factors of 657 are 1, 3, 9, 73, 219, 657
The factors of 769 are 1, 769
The HCF of 657,769 is 1.
Lets's calculate GCF of 657,769
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 657
:1,3,9,73,219,657
Now, list down the factors of 769
:1,769
Greatest Common Factor
We found the factors 657,769 . The biggest common factor number is the GCF number.
So the greatest common factor 657,769 is 1.
Lets's calculate LCM of 540,360
2 | 540, 360 |
2 | 270, 180 |
3 | 135, 90 |
3 | 45, 30 |
5 | 15, 10 |
3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 3 x 2 = 1080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1080
Therefore, the GCF of Fractions 657/540,769/360 is 1/1080
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 540,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,360) = 180
common factors(in case of two or more numbers have common factors) = 1
GCF(540,360) x common factors =180 x 1 = 180
LCM(540,360) = ( 540 × 360 ) / 180
LCM(540,360) = 194400 / 180
LCM(540,360) = 1080
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 657,769?
The HCF of 657,769 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 657/540, 769/360?
Answer: GCF of Numerators as per given numbers 657/540, 769/360 is
GCF of Numerators i.e. for 657,769 is 1
LCM of denominators i.e. for 540,360 is 1080.
Thus, GCF of Fractions is 1/1080.Finally, GCF of Fractions for 657/540, 769/360 is 1/1080.