Use our free GCF of Fractions Calculator tool to compute the GCF of 237/768, 228/680 i.e 3/65280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 237/768, 228/680.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 237/768,228/680
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 237/768,228/680, numerators are 237,228
Denominators are 768,680
The GCF of 237,228 is 3 .
LCM of 768,680 is 65280.
The greatest common factor of 237/768,228/680 = [GCF of 237,228]/[LCM of 768,680]= 3/65280
Therefore, the GCF of 237/768,228/680 is 3/65280.
To find the highest common factor of 237,228, 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 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The HCF of 237,228 is 3.
Lets's calculate GCF of 237,228
3 | 237, 228 |
79, 76 |
∴ 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 228
:1,2,3,4,6,12,19,38,57,76,114,228
Greatest Common Factor
We found the factors 237,228 . The biggest common factor number is the GCF number.
So the greatest common factor 237,228 is 3.
Lets's calculate LCM of 768,680
2 | 768, 680 |
2 | 384, 340 |
2 | 192, 170 |
96, 85 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 96 x 85 = 65280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/65280
Therefore, the GCF of Fractions 237/768,228/680 is 3/65280
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 768,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,680) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(768,680) x common factors =8 x 1 = 8
LCM(768,680) = ( 768 × 680 ) / 8
LCM(768,680) = 522240 / 8
LCM(768,680) = 65280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 237,228?
The HCF of 237,228 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 237/768, 228/680?
Answer: GCF of Numerators as per given numbers 237/768, 228/680 is
GCF of Numerators i.e. for 237,228 is 3
LCM of denominators i.e. for 768,680 is 65280.
Thus, GCF of Fractions is 3/65280.Finally, GCF of Fractions for 237/768, 228/680 is 3/65280.