Use our free GCF of Fractions Calculator tool to compute the GCF of 780/653, 500/548 i.e 20/357844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/653, 500/548.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 780/653,500/548
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 780/653,500/548, numerators are 780,500
Denominators are 653,548
The GCF of 780,500 is 20 .
LCM of 653,548 is 357844.
The greatest common factor of 780/653,500/548 = [GCF of 780,500]/[LCM of 653,548]= 20/357844
Therefore, the GCF of 780/653,500/548 is 20/357844.
To find the highest common factor of 780,500, we have to find the factors of both numbers and list the highest common factor.
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The HCF of 780,500 is 20.
Lets's calculate GCF of 780,500
2 | 780, 500 |
2 | 390, 250 |
5 | 195, 125 |
39, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
Greatest Common Factor
We found the factors 780,500 . The biggest common factor number is the GCF number.
So the greatest common factor 780,500 is 20.
Lets's calculate LCM of 653,548
Given numbers has no common factors except 1. So, there LCM is their product i.e 357844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/357844
Therefore, the GCF of Fractions 780/653,500/548 is 20/357844
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 653,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(653,548) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(653,548) x common factors =1 x 1 = 1
LCM(653,548) = ( 653 × 548 ) / 1
LCM(653,548) = 357844 / 1
LCM(653,548) = 357844
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 780,500?
The HCF of 780,500 is 20
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 780/653, 500/548?
Answer: GCF of Numerators as per given numbers 780/653, 500/548 is
GCF of Numerators i.e. for 780,500 is 20
LCM of denominators i.e. for 653,548 is 357844.
Thus, GCF of Fractions is 20/357844.Finally, GCF of Fractions for 780/653, 500/548 is 20/357844.