Use our free GCF of Fractions Calculator tool to compute the GCF of 208/468, 980/768 i.e 4/29952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 208/468, 980/768.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 208/468,980/768
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 208/468,980/768, numerators are 208,980
Denominators are 468,768
The GCF of 208,980 is 4 .
LCM of 468,768 is 29952.
The greatest common factor of 208/468,980/768 = [GCF of 208,980]/[LCM of 468,768]= 4/29952
Therefore, the GCF of 208/468,980/768 is 4/29952.
To find the highest common factor of 208,980, we have to find the factors of both numbers and list the highest common factor.
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The HCF of 208,980 is 4.
Lets's calculate GCF of 208,980
2 | 208, 980 |
2 | 104, 490 |
52, 245 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Greatest Common Factor
We found the factors 208,980 . The biggest common factor number is the GCF number.
So the greatest common factor 208,980 is 4.
Lets's calculate LCM of 468,768
2 | 468, 768 |
2 | 234, 384 |
3 | 117, 192 |
39, 64 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 39 x 64 = 29952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/29952
Therefore, the GCF of Fractions 208/468,980/768 is 4/29952
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 468,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(468,768) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(468,768) x common factors =12 x 1 = 12
LCM(468,768) = ( 468 × 768 ) / 12
LCM(468,768) = 359424 / 12
LCM(468,768) = 29952
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 208,980?
The HCF of 208,980 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 208/468, 980/768?
Answer: GCF of Numerators as per given numbers 208/468, 980/768 is
GCF of Numerators i.e. for 208,980 is 4
LCM of denominators i.e. for 468,768 is 29952.
Thus, GCF of Fractions is 4/29952.Finally, GCF of Fractions for 208/468, 980/768 is 4/29952.