Use our free GCF of Fractions Calculator tool to compute the GCF of 624/34, 585/2784 i.e 39/47328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 624/34, 585/2784.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 624/34,585/2784
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 624/34,585/2784, numerators are 624,585
Denominators are 34,2784
The GCF of 624,585 is 39 .
LCM of 34,2784 is 47328.
The greatest common factor of 624/34,585/2784 = [GCF of 624,585]/[LCM of 34,2784]= 39/47328
Therefore, the GCF of 624/34,585/2784 is 39/47328.
To find the highest common factor of 624,585, we have to find the factors of both numbers and list the highest common factor.
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
The HCF of 624,585 is 39.
Lets's calculate GCF of 624,585
3 | 624, 585 |
13 | 208, 195 |
16, 15 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Now, list down the factors of 585
:1,3,5,9,13,15,39,45,65,117,195,585
Greatest Common Factor
We found the factors 624,585 . The biggest common factor number is the GCF number.
So the greatest common factor 624,585 is 39.
Lets's calculate LCM of 34,2784
2 | 34, 2784 |
17, 1392 |
∴ So the LCM of the given numbers is 2 x 17 x 1392 = 47328
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/47328
Therefore, the GCF of Fractions 624/34,585/2784 is 39/47328
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 34,2784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,2784) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,2784) x common factors =2 x 1 = 2
LCM(34,2784) = ( 34 × 2784 ) / 2
LCM(34,2784) = 94656 / 2
LCM(34,2784) = 47328
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 624,585?
The HCF of 624,585 is 39
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 624/34, 585/2784?
Answer: GCF of Numerators as per given numbers 624/34, 585/2784 is
GCF of Numerators i.e. for 624,585 is 39
LCM of denominators i.e. for 34,2784 is 47328.
Thus, GCF of Fractions is 39/47328.Finally, GCF of Fractions for 624/34, 585/2784 is 39/47328.