Use our free GCF of Fractions Calculator tool to compute the GCF of 280/220, 592/408 i.e 8/22440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/220, 592/408.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 280/220,592/408
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 280/220,592/408, numerators are 280,592
Denominators are 220,408
The GCF of 280,592 is 8 .
LCM of 220,408 is 22440.
The greatest common factor of 280/220,592/408 = [GCF of 280,592]/[LCM of 220,408]= 8/22440
Therefore, the GCF of 280/220,592/408 is 8/22440.
To find the highest common factor of 280,592, we have to find the factors of both numbers and list the highest common factor.
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The HCF of 280,592 is 8.
Lets's calculate GCF of 280,592
2 | 280, 592 |
2 | 140, 296 |
2 | 70, 148 |
35, 74 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Greatest Common Factor
We found the factors 280,592 . The biggest common factor number is the GCF number.
So the greatest common factor 280,592 is 8.
Lets's calculate LCM of 220,408
2 | 220, 408 |
2 | 110, 204 |
55, 102 |
∴ So the LCM of the given numbers is 2 x 2 x 55 x 102 = 22440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/22440
Therefore, the GCF of Fractions 280/220,592/408 is 8/22440
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 220,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(220,408) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(220,408) x common factors =4 x 1 = 4
LCM(220,408) = ( 220 × 408 ) / 4
LCM(220,408) = 89760 / 4
LCM(220,408) = 22440
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 280,592?
The HCF of 280,592 is 8
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 280/220, 592/408?
Answer: GCF of Numerators as per given numbers 280/220, 592/408 is
GCF of Numerators i.e. for 280,592 is 8
LCM of denominators i.e. for 220,408 is 22440.
Thus, GCF of Fractions is 8/22440.Finally, GCF of Fractions for 280/220, 592/408 is 8/22440.