Use our free GCF of Fractions Calculator tool to compute the GCF of 84/232, 14/280, 604/460 i.e 2/186760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/232, 14/280, 604/460.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/232,14/280,604/460
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 84/232,14/280,604/460, numerators are 84,14,604
Denominators are 232,280,460
The GCF of 84,14,604 is 2 .
LCM of 232,280,460 is 186760.
The greatest common factor of 84/232,14/280,604/460 = [GCF of 84,14,604]/[LCM of 232,280,460]= 2/186760
Therefore, the GCF of 84/232,14/280,604/460 is 2/186760.
To find the highest common factor of 84,14,604, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 14 are 1, 2, 7, 14
The factors of 604 are 1, 2, 4, 151, 302, 604
The HCF of 84,14,604 is 2.
Lets's calculate GCF of 84,14,604
2 | 84, 14, 604 |
42, 7, 302 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 604
:1,2,4,151,302,604
Greatest Common Factor
We found the factors 84,14,604 . The biggest common factor number is the GCF number.
So the greatest common factor 84,14,604 is 2.
Lets's calculate LCM of 232,280,460
2 | 232, 280, 460 |
2 | 116, 140, 230 |
2 | 58, 70, 115 |
5 | 29, 35, 115 |
29, 7, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 29 x 7 x 23 = 186760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/186760
Therefore, the GCF of Fractions 84/232,14/280,604/460 is 2/186760
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 232,280,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(232,280,460) = 4
common factors(in case of two or more numbers have common factors) = 40
GCF(232,280,460) x common factors =4 x 40 = 160
LCM(232,280,460) = ( 232 × 280 × 460 ) / 160
LCM(232,280,460) = 29881600 / 160
LCM(232,280,460) = 186760
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 84,14,604?
The HCF of 84,14,604 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 84/232, 14/280, 604/460?
Answer: GCF of Numerators as per given numbers 84/232, 14/280, 604/460 is
GCF of Numerators i.e. for 84,14,604 is 2
LCM of denominators i.e. for 232,280,460 is 186760.
Thus, GCF of Fractions is 2/186760.Finally, GCF of Fractions for 84/232, 14/280, 604/460 is 2/186760.