Use our free GCF of Fractions Calculator tool to compute the GCF of 5209/560, 3268/3000 i.e 1/42000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5209/560, 3268/3000.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5209/560,3268/3000
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 5209/560,3268/3000, numerators are 5209,3268
Denominators are 560,3000
The GCF of 5209,3268 is 1 .
LCM of 560,3000 is 42000.
The greatest common factor of 5209/560,3268/3000 = [GCF of 5209,3268]/[LCM of 560,3000]= 1/42000
Therefore, the GCF of 5209/560,3268/3000 is 1/42000.
To find the highest common factor of 5209,3268, we have to find the factors of both numbers and list the highest common factor.
The factors of 5209 are 1, 5209
The factors of 3268 are 1, 2, 4, 19, 38, 43, 76, 86, 172, 817, 1634, 3268
The HCF of 5209,3268 is 1.
Lets's calculate GCF of 5209,3268
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 5209
:1,5209
Now, list down the factors of 3268
:1,2,4,19,38,43,76,86,172,817,1634,3268
Greatest Common Factor
We found the factors 5209,3268 . The biggest common factor number is the GCF number.
So the greatest common factor 5209,3268 is 1.
Lets's calculate LCM of 560,3000
2 | 560, 3000 |
2 | 280, 1500 |
2 | 140, 750 |
5 | 70, 375 |
14, 75 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 14 x 75 = 42000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42000
Therefore, the GCF of Fractions 5209/560,3268/3000 is 1/42000
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 560,3000 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(560,3000) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(560,3000) x common factors =40 x 1 = 40
LCM(560,3000) = ( 560 × 3000 ) / 40
LCM(560,3000) = 1680000 / 40
LCM(560,3000) = 42000
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5209,3268?
The HCF of 5209,3268 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 5209/560, 3268/3000?
Answer: GCF of Numerators as per given numbers 5209/560, 3268/3000 is
GCF of Numerators i.e. for 5209,3268 is 1
LCM of denominators i.e. for 560,3000 is 42000.
Thus, GCF of Fractions is 1/42000.Finally, GCF of Fractions for 5209/560, 3268/3000 is 1/42000.