Use our free GCF of Fractions Calculator tool to compute the GCF of 28/53, 616/30, 748/212 i.e 4/3180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/53, 616/30, 748/212.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/53,616/30,748/212
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 28/53,616/30,748/212, numerators are 28,616,748
Denominators are 53,30,212
The GCF of 28,616,748 is 4 .
LCM of 53,30,212 is 3180.
The greatest common factor of 28/53,616/30,748/212 = [GCF of 28,616,748]/[LCM of 53,30,212]= 4/3180
Therefore, the GCF of 28/53,616/30,748/212 is 4/3180.
To find the highest common factor of 28,616,748, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 28,616,748 is 4.
Lets's calculate GCF of 28,616,748
2 | 28, 616, 748 |
2 | 14, 308, 374 |
7, 154, 187 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 28,616,748 . The biggest common factor number is the GCF number.
So the greatest common factor 28,616,748 is 4.
Lets's calculate LCM of 53,30,212
2 | 53, 30, 212 |
53 | 53, 15, 106 |
1, 15, 2 |
∴ So the LCM of the given numbers is 2 x 53 x 1 x 15 x 2 = 3180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3180
Therefore, the GCF of Fractions 28/53,616/30,748/212 is 4/3180
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 53,30,212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,30,212) = 1
common factors(in case of two or more numbers have common factors) = 106
GCF(53,30,212) x common factors =1 x 106 = 106
LCM(53,30,212) = ( 53 × 30 × 212 ) / 106
LCM(53,30,212) = 337080 / 106
LCM(53,30,212) = 3180
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 28,616,748?
The HCF of 28,616,748 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 28/53, 616/30, 748/212?
Answer: GCF of Numerators as per given numbers 28/53, 616/30, 748/212 is
GCF of Numerators i.e. for 28,616,748 is 4
LCM of denominators i.e. for 53,30,212 is 3180.
Thus, GCF of Fractions is 4/3180.Finally, GCF of Fractions for 28/53, 616/30, 748/212 is 4/3180.