Use our free GCF of Fractions Calculator tool to compute the GCF of 108/284, 140/510, 608/735 i.e 4/3548580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/284, 140/510, 608/735.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 108/284,140/510,608/735
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 108/284,140/510,608/735, numerators are 108,140,608
Denominators are 284,510,735
The GCF of 108,140,608 is 4 .
LCM of 284,510,735 is 3548580.
The greatest common factor of 108/284,140/510,608/735 = [GCF of 108,140,608]/[LCM of 284,510,735]= 4/3548580
Therefore, the GCF of 108/284,140/510,608/735 is 4/3548580.
To find the highest common factor of 108,140,608, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
The HCF of 108,140,608 is 4.
Lets's calculate GCF of 108,140,608
2 | 108, 140, 608 |
2 | 54, 70, 304 |
27, 35, 152 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Now, list down the factors of 608
:1,2,4,8,16,19,32,38,76,152,304,608
Greatest Common Factor
We found the factors 108,140,608 . The biggest common factor number is the GCF number.
So the greatest common factor 108,140,608 is 4.
Lets's calculate LCM of 284,510,735
2 | 284, 510, 735 |
3 | 142, 255, 735 |
5 | 142, 85, 245 |
142, 17, 49 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 142 x 17 x 49 = 3548580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3548580
Therefore, the GCF of Fractions 108/284,140/510,608/735 is 4/3548580
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 284,510,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,510,735) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(284,510,735) x common factors =1 x 30 = 30
LCM(284,510,735) = ( 284 × 510 × 735 ) / 30
LCM(284,510,735) = 106457400 / 30
LCM(284,510,735) = 3548580
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 108,140,608?
The HCF of 108,140,608 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 108/284, 140/510, 608/735?
Answer: GCF of Numerators as per given numbers 108/284, 140/510, 608/735 is
GCF of Numerators i.e. for 108,140,608 is 4
LCM of denominators i.e. for 284,510,735 is 3548580.
Thus, GCF of Fractions is 4/3548580.Finally, GCF of Fractions for 108/284, 140/510, 608/735 is 4/3548580.