Use our free GCF of Fractions Calculator tool to compute the GCF of 280/764, 414/954 i.e 2/364428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/764, 414/954.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 280/764,414/954
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 280/764,414/954, numerators are 280,414
Denominators are 764,954
The GCF of 280,414 is 2 .
LCM of 764,954 is 364428.
The greatest common factor of 280/764,414/954 = [GCF of 280,414]/[LCM of 764,954]= 2/364428
Therefore, the GCF of 280/764,414/954 is 2/364428.
To find the highest common factor of 280,414, 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 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 280,414 is 2.
Lets's calculate GCF of 280,414
2 | 280, 414 |
140, 207 |
∴ 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 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 280,414 . The biggest common factor number is the GCF number.
So the greatest common factor 280,414 is 2.
Lets's calculate LCM of 764,954
2 | 764, 954 |
382, 477 |
∴ So the LCM of the given numbers is 2 x 382 x 477 = 364428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/364428
Therefore, the GCF of Fractions 280/764,414/954 is 2/364428
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 764,954 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(764,954) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(764,954) x common factors =2 x 1 = 2
LCM(764,954) = ( 764 × 954 ) / 2
LCM(764,954) = 728856 / 2
LCM(764,954) = 364428
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 280,414?
The HCF of 280,414 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 280/764, 414/954?
Answer: GCF of Numerators as per given numbers 280/764, 414/954 is
GCF of Numerators i.e. for 280,414 is 2
LCM of denominators i.e. for 764,954 is 364428.
Thus, GCF of Fractions is 2/364428.Finally, GCF of Fractions for 280/764, 414/954 is 2/364428.