Use our free GCF of Fractions Calculator tool to compute the GCF of 768/722, 654/278 i.e 6/100358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/722, 654/278.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 768/722,654/278
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 768/722,654/278, numerators are 768,654
Denominators are 722,278
The GCF of 768,654 is 6 .
LCM of 722,278 is 100358.
The greatest common factor of 768/722,654/278 = [GCF of 768,654]/[LCM of 722,278]= 6/100358
Therefore, the GCF of 768/722,654/278 is 6/100358.
To find the highest common factor of 768,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 768,654 is 6.
Lets's calculate GCF of 768,654
2 | 768, 654 |
3 | 384, 327 |
128, 109 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 768,654 . The biggest common factor number is the GCF number.
So the greatest common factor 768,654 is 6.
Lets's calculate LCM of 722,278
2 | 722, 278 |
361, 139 |
∴ So the LCM of the given numbers is 2 x 361 x 139 = 100358
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/100358
Therefore, the GCF of Fractions 768/722,654/278 is 6/100358
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 722,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(722,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(722,278) x common factors =2 x 1 = 2
LCM(722,278) = ( 722 × 278 ) / 2
LCM(722,278) = 200716 / 2
LCM(722,278) = 100358
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 768,654?
The HCF of 768,654 is 6
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 768/722, 654/278?
Answer: GCF of Numerators as per given numbers 768/722, 654/278 is
GCF of Numerators i.e. for 768,654 is 6
LCM of denominators i.e. for 722,278 is 100358.
Thus, GCF of Fractions is 6/100358.Finally, GCF of Fractions for 768/722, 654/278 is 6/100358.