Use our free GCF of Fractions Calculator tool to compute the GCF of 280/431, 542/672 i.e 2/289632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/431, 542/672.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 280/431,542/672
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 280/431,542/672, numerators are 280,542
Denominators are 431,672
The GCF of 280,542 is 2 .
LCM of 431,672 is 289632.
The greatest common factor of 280/431,542/672 = [GCF of 280,542]/[LCM of 431,672]= 2/289632
Therefore, the GCF of 280/431,542/672 is 2/289632.
To find the highest common factor of 280,542, 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 542 are 1, 2, 271, 542
The HCF of 280,542 is 2.
Lets's calculate GCF of 280,542
2 | 280, 542 |
140, 271 |
∴ So the GCF of the given numbers is 2 = 2
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 542
:1,2,271,542
Greatest Common Factor
We found the factors 280,542 . The biggest common factor number is the GCF number.
So the greatest common factor 280,542 is 2.
Lets's calculate LCM of 431,672
Given numbers has no common factors except 1. So, there LCM is their product i.e 289632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/289632
Therefore, the GCF of Fractions 280/431,542/672 is 2/289632
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 431,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(431,672) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(431,672) x common factors =1 x 1 = 1
LCM(431,672) = ( 431 × 672 ) / 1
LCM(431,672) = 289632 / 1
LCM(431,672) = 289632
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 280,542?
The HCF of 280,542 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 280/431, 542/672?
Answer: GCF of Numerators as per given numbers 280/431, 542/672 is
GCF of Numerators i.e. for 280,542 is 2
LCM of denominators i.e. for 431,672 is 289632.
Thus, GCF of Fractions is 2/289632.Finally, GCF of Fractions for 280/431, 542/672 is 2/289632.