Use our free GCF of Fractions Calculator tool to compute the GCF of 431/976, 720/584 i.e 1/71248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 431/976, 720/584.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 431/976,720/584
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 431/976,720/584, numerators are 431,720
Denominators are 976,584
The GCF of 431,720 is 1 .
LCM of 976,584 is 71248.
The greatest common factor of 431/976,720/584 = [GCF of 431,720]/[LCM of 976,584]= 1/71248
Therefore, the GCF of 431/976,720/584 is 1/71248.
To find the highest common factor of 431,720, we have to find the factors of both numbers and list the highest common factor.
The factors of 431 are 1, 431
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The HCF of 431,720 is 1.
Lets's calculate GCF of 431,720
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 431
:1,431
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Greatest Common Factor
We found the factors 431,720 . The biggest common factor number is the GCF number.
So the greatest common factor 431,720 is 1.
Lets's calculate LCM of 976,584
2 | 976, 584 |
2 | 488, 292 |
2 | 244, 146 |
122, 73 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 122 x 73 = 71248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71248
Therefore, the GCF of Fractions 431/976,720/584 is 1/71248
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 976,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(976,584) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(976,584) x common factors =8 x 1 = 8
LCM(976,584) = ( 976 × 584 ) / 8
LCM(976,584) = 569984 / 8
LCM(976,584) = 71248
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 431,720?
The HCF of 431,720 is 1
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 431/976, 720/584?
Answer: GCF of Numerators as per given numbers 431/976, 720/584 is
GCF of Numerators i.e. for 431,720 is 1
LCM of denominators i.e. for 976,584 is 71248.
Thus, GCF of Fractions is 1/71248.Finally, GCF of Fractions for 431/976, 720/584 is 1/71248.