Use our free GCF of Fractions Calculator tool to compute the GCF of 380/846, 312/618 i.e 4/87138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 380/846, 312/618.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 380/846,312/618
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 380/846,312/618, numerators are 380,312
Denominators are 846,618
The GCF of 380,312 is 4 .
LCM of 846,618 is 87138.
The greatest common factor of 380/846,312/618 = [GCF of 380,312]/[LCM of 846,618]= 4/87138
Therefore, the GCF of 380/846,312/618 is 4/87138.
To find the highest common factor of 380,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 380,312 is 4.
Lets's calculate GCF of 380,312
2 | 380, 312 |
2 | 190, 156 |
95, 78 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 380,312 . The biggest common factor number is the GCF number.
So the greatest common factor 380,312 is 4.
Lets's calculate LCM of 846,618
2 | 846, 618 |
3 | 423, 309 |
141, 103 |
∴ So the LCM of the given numbers is 2 x 3 x 141 x 103 = 87138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/87138
Therefore, the GCF of Fractions 380/846,312/618 is 4/87138
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 846,618 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(846,618) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(846,618) x common factors =6 x 1 = 6
LCM(846,618) = ( 846 × 618 ) / 6
LCM(846,618) = 522828 / 6
LCM(846,618) = 87138
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 380,312?
The HCF of 380,312 is 4
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 380/846, 312/618?
Answer: GCF of Numerators as per given numbers 380/846, 312/618 is
GCF of Numerators i.e. for 380,312 is 4
LCM of denominators i.e. for 846,618 is 87138.
Thus, GCF of Fractions is 4/87138.Finally, GCF of Fractions for 380/846, 312/618 is 4/87138.