Use our free GCF of Fractions Calculator tool to compute the GCF of 78/748, 430/812, 556/948 i.e 2/35987028 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/748, 430/812, 556/948.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/748,430/812,556/948
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 78/748,430/812,556/948, numerators are 78,430,556
Denominators are 748,812,948
The GCF of 78,430,556 is 2 .
LCM of 748,812,948 is 35987028.
The greatest common factor of 78/748,430/812,556/948 = [GCF of 78,430,556]/[LCM of 748,812,948]= 2/35987028
Therefore, the GCF of 78/748,430/812,556/948 is 2/35987028.
To find the highest common factor of 78,430,556, 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 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 556 are 1, 2, 4, 139, 278, 556
The HCF of 78,430,556 is 2.
Lets's calculate GCF of 78,430,556
2 | 78, 430, 556 |
39, 215, 278 |
∴ 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 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 556
:1,2,4,139,278,556
Greatest Common Factor
We found the factors 78,430,556 . The biggest common factor number is the GCF number.
So the greatest common factor 78,430,556 is 2.
Lets's calculate LCM of 748,812,948
2 | 748, 812, 948 |
2 | 374, 406, 474 |
187, 203, 237 |
∴ So the LCM of the given numbers is 2 x 2 x 187 x 203 x 237 = 35987028
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35987028
Therefore, the GCF of Fractions 78/748,430/812,556/948 is 2/35987028
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 748,812,948 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,812,948) = 4
common factors(in case of two or more numbers have common factors) = 4
GCF(748,812,948) x common factors =4 x 4 = 16
LCM(748,812,948) = ( 748 × 812 × 948 ) / 16
LCM(748,812,948) = 575792448 / 16
LCM(748,812,948) = 35987028
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,430,556?
The HCF of 78,430,556 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 78/748, 430/812, 556/948?
Answer: GCF of Numerators as per given numbers 78/748, 430/812, 556/948 is
GCF of Numerators i.e. for 78,430,556 is 2
LCM of denominators i.e. for 748,812,948 is 35987028.
Thus, GCF of Fractions is 2/35987028.Finally, GCF of Fractions for 78/748, 430/812, 556/948 is 2/35987028.