Use our free GCF of Fractions Calculator tool to compute the GCF of 78/49, 984/20, 598/512 i.e 2/125440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/49, 984/20, 598/512.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/49,984/20,598/512
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 78/49,984/20,598/512, numerators are 78,984,598
Denominators are 49,20,512
The GCF of 78,984,598 is 2 .
LCM of 49,20,512 is 125440.
The greatest common factor of 78/49,984/20,598/512 = [GCF of 78,984,598]/[LCM of 49,20,512]= 2/125440
Therefore, the GCF of 78/49,984/20,598/512 is 2/125440.
To find the highest common factor of 78,984,598, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598
The HCF of 78,984,598 is 2.
Lets's calculate GCF of 78,984,598
2 | 78, 984, 598 |
39, 492, 299 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Now, list down the factors of 598
:1,2,13,23,26,46,299,598
Greatest Common Factor
We found the factors 78,984,598 . The biggest common factor number is the GCF number.
So the greatest common factor 78,984,598 is 2.
Lets's calculate LCM of 49,20,512
2 | 49, 20, 512 |
2 | 49, 10, 256 |
49, 5, 128 |
∴ So the LCM of the given numbers is 2 x 2 x 49 x 5 x 128 = 125440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/125440
Therefore, the GCF of Fractions 78/49,984/20,598/512 is 2/125440
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 49,20,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,20,512) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(49,20,512) x common factors =1 x 4 = 4
LCM(49,20,512) = ( 49 × 20 × 512 ) / 4
LCM(49,20,512) = 501760 / 4
LCM(49,20,512) = 125440
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,984,598?
The HCF of 78,984,598 is 2
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 78/49, 984/20, 598/512?
Answer: GCF of Numerators as per given numbers 78/49, 984/20, 598/512 is
GCF of Numerators i.e. for 78,984,598 is 2
LCM of denominators i.e. for 49,20,512 is 125440.
Thus, GCF of Fractions is 2/125440.Finally, GCF of Fractions for 78/49, 984/20, 598/512 is 2/125440.