Use our free GCF of Fractions Calculator tool to compute the GCF of 524/418, 780/750 i.e 4/156750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 524/418, 780/750.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 524/418,780/750
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 524/418,780/750, numerators are 524,780
Denominators are 418,750
The GCF of 524,780 is 4 .
LCM of 418,750 is 156750.
The greatest common factor of 524/418,780/750 = [GCF of 524,780]/[LCM of 418,750]= 4/156750
Therefore, the GCF of 524/418,780/750 is 4/156750.
To find the highest common factor of 524,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 524 are 1, 2, 4, 131, 262, 524
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 HCF of 524,780 is 4.
Lets's calculate GCF of 524,780
2 | 524, 780 |
2 | 262, 390 |
131, 195 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 524
:1,2,4,131,262,524
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
Greatest Common Factor
We found the factors 524,780 . The biggest common factor number is the GCF number.
So the greatest common factor 524,780 is 4.
Lets's calculate LCM of 418,750
2 | 418, 750 |
209, 375 |
∴ So the LCM of the given numbers is 2 x 209 x 375 = 156750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/156750
Therefore, the GCF of Fractions 524/418,780/750 is 4/156750
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 418,750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(418,750) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(418,750) x common factors =2 x 1 = 2
LCM(418,750) = ( 418 × 750 ) / 2
LCM(418,750) = 313500 / 2
LCM(418,750) = 156750
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 524,780?
The HCF of 524,780 is 4
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 524/418, 780/750?
Answer: GCF of Numerators as per given numbers 524/418, 780/750 is
GCF of Numerators i.e. for 524,780 is 4
LCM of denominators i.e. for 418,750 is 156750.
Thus, GCF of Fractions is 4/156750.Finally, GCF of Fractions for 524/418, 780/750 is 4/156750.