Use our free GCF of Fractions Calculator tool to compute the GCF of 237/865, 684/300 i.e 3/51900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 237/865, 684/300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 237/865,684/300
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 237/865,684/300, numerators are 237,684
Denominators are 865,300
The GCF of 237,684 is 3 .
LCM of 865,300 is 51900.
The greatest common factor of 237/865,684/300 = [GCF of 237,684]/[LCM of 865,300]= 3/51900
Therefore, the GCF of 237/865,684/300 is 3/51900.
To find the highest common factor of 237,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 237 are 1, 3, 79, 237
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 237,684 is 3.
Lets's calculate GCF of 237,684
3 | 237, 684 |
79, 228 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 237
:1,3,79,237
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 237,684 . The biggest common factor number is the GCF number.
So the greatest common factor 237,684 is 3.
Lets's calculate LCM of 865,300
5 | 865, 300 |
173, 60 |
∴ So the LCM of the given numbers is 5 x 173 x 60 = 51900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/51900
Therefore, the GCF of Fractions 237/865,684/300 is 3/51900
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 865,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(865,300) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(865,300) x common factors =5 x 1 = 5
LCM(865,300) = ( 865 × 300 ) / 5
LCM(865,300) = 259500 / 5
LCM(865,300) = 51900
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 237,684?
The HCF of 237,684 is 3
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 237/865, 684/300?
Answer: GCF of Numerators as per given numbers 237/865, 684/300 is
GCF of Numerators i.e. for 237,684 is 3
LCM of denominators i.e. for 865,300 is 51900.
Thus, GCF of Fractions is 3/51900.Finally, GCF of Fractions for 237/865, 684/300 is 3/51900.