Use our free GCF of Fractions Calculator tool to compute the GCF of 5224/678, 7638/148 i.e 2/50172 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5224/678, 7638/148.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5224/678,7638/148
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 5224/678,7638/148, numerators are 5224,7638
Denominators are 678,148
The GCF of 5224,7638 is 2 .
LCM of 678,148 is 50172.
The greatest common factor of 5224/678,7638/148 = [GCF of 5224,7638]/[LCM of 678,148]= 2/50172
Therefore, the GCF of 5224/678,7638/148 is 2/50172.
To find the highest common factor of 5224,7638, we have to find the factors of both numbers and list the highest common factor.
The factors of 5224 are 1, 2, 4, 8, 653, 1306, 2612, 5224
The factors of 7638 are 1, 2, 3, 6, 19, 38, 57, 67, 114, 134, 201, 402, 1273, 2546, 3819, 7638
The HCF of 5224,7638 is 2.
Lets's calculate GCF of 5224,7638
2 | 5224, 7638 |
2612, 3819 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 5224
:1,2,4,8,653,1306,2612,5224
Now, list down the factors of 7638
:1,2,3,6,19,38,57,67,114,134,201,402,1273,2546,3819,7638
Greatest Common Factor
We found the factors 5224,7638 . The biggest common factor number is the GCF number.
So the greatest common factor 5224,7638 is 2.
Lets's calculate LCM of 678,148
2 | 678, 148 |
339, 74 |
∴ So the LCM of the given numbers is 2 x 339 x 74 = 50172
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/50172
Therefore, the GCF of Fractions 5224/678,7638/148 is 2/50172
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 678,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,148) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,148) x common factors =2 x 1 = 2
LCM(678,148) = ( 678 × 148 ) / 2
LCM(678,148) = 100344 / 2
LCM(678,148) = 50172
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5224,7638?
The HCF of 5224,7638 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 5224/678, 7638/148?
Answer: GCF of Numerators as per given numbers 5224/678, 7638/148 is
GCF of Numerators i.e. for 5224,7638 is 2
LCM of denominators i.e. for 678,148 is 50172.
Thus, GCF of Fractions is 2/50172.Finally, GCF of Fractions for 5224/678, 7638/148 is 2/50172.