Use our free GCF of Fractions Calculator tool to compute the GCF of 49/706, 219/416, 557/308 i.e 1/11307296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/706, 219/416, 557/308.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 49/706,219/416,557/308
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 49/706,219/416,557/308, numerators are 49,219,557
Denominators are 706,416,308
The GCF of 49,219,557 is 1 .
LCM of 706,416,308 is 11307296.
The greatest common factor of 49/706,219/416,557/308 = [GCF of 49,219,557]/[LCM of 706,416,308]= 1/11307296
Therefore, the GCF of 49/706,219/416,557/308 is 1/11307296.
To find the highest common factor of 49,219,557, we have to find the factors of both numbers and list the highest common factor.
The factors of 49 are 1, 7, 49
The factors of 219 are 1, 3, 73, 219
The factors of 557 are 1, 557
The HCF of 49,219,557 is 1.
Lets's calculate GCF of 49,219,557
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 219
:1,3,73,219
Now, list down the factors of 557
:1,557
Greatest Common Factor
We found the factors 49,219,557 . The biggest common factor number is the GCF number.
So the greatest common factor 49,219,557 is 1.
Lets's calculate LCM of 706,416,308
2 | 706, 416, 308 |
2 | 353, 208, 154 |
353, 104, 77 |
∴ So the LCM of the given numbers is 2 x 2 x 353 x 104 x 77 = 11307296
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11307296
Therefore, the GCF of Fractions 49/706,219/416,557/308 is 1/11307296
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 706,416,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,416,308) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(706,416,308) x common factors =2 x 4 = 8
LCM(706,416,308) = ( 706 × 416 × 308 ) / 8
LCM(706,416,308) = 90458368 / 8
LCM(706,416,308) = 11307296
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 49,219,557?
The HCF of 49,219,557 is 1
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 49/706, 219/416, 557/308?
Answer: GCF of Numerators as per given numbers 49/706, 219/416, 557/308 is
GCF of Numerators i.e. for 49,219,557 is 1
LCM of denominators i.e. for 706,416,308 is 11307296.
Thus, GCF of Fractions is 1/11307296.Finally, GCF of Fractions for 49/706, 219/416, 557/308 is 1/11307296.