Use our free GCF of Fractions Calculator tool to compute the GCF of 10/414, 76/830, 112/270 i.e 2/515430 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/414, 76/830, 112/270.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 10/414,76/830,112/270
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 10/414,76/830,112/270, numerators are 10,76,112
Denominators are 414,830,270
The GCF of 10,76,112 is 2 .
LCM of 414,830,270 is 515430.
The greatest common factor of 10/414,76/830,112/270 = [GCF of 10,76,112]/[LCM of 414,830,270]= 2/515430
Therefore, the GCF of 10/414,76/830,112/270 is 2/515430.
To find the highest common factor of 10,76,112, we have to find the factors of both numbers and list the highest common factor.
The factors of 10 are 1, 2, 5, 10
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The HCF of 10,76,112 is 2.
Lets's calculate GCF of 10,76,112
2 | 10, 76, 112 |
5, 38, 56 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Greatest Common Factor
We found the factors 10,76,112 . The biggest common factor number is the GCF number.
So the greatest common factor 10,76,112 is 2.
Lets's calculate LCM of 414,830,270
2 | 414, 830, 270 |
3 | 207, 415, 135 |
3 | 69, 415, 45 |
5 | 23, 415, 15 |
23, 83, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 23 x 83 x 3 = 515430
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/515430
Therefore, the GCF of Fractions 10/414,76/830,112/270 is 2/515430
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 414,830,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,830,270) = 2
common factors(in case of two or more numbers have common factors) = 90
GCF(414,830,270) x common factors =2 x 90 = 180
LCM(414,830,270) = ( 414 × 830 × 270 ) / 180
LCM(414,830,270) = 92777400 / 180
LCM(414,830,270) = 515430
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 10,76,112?
The HCF of 10,76,112 is 2
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 10/414, 76/830, 112/270?
Answer: GCF of Numerators as per given numbers 10/414, 76/830, 112/270 is
GCF of Numerators i.e. for 10,76,112 is 2
LCM of denominators i.e. for 414,830,270 is 515430.
Thus, GCF of Fractions is 2/515430.Finally, GCF of Fractions for 10/414, 76/830, 112/270 is 2/515430.