Use our free GCF of Fractions Calculator tool to compute the GCF of 6/47, 30/72, 96/368, 346/112 i.e 2/1089648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/47, 30/72, 96/368, 346/112.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6/47,30/72,96/368,346/112
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 6/47,30/72,96/368,346/112, numerators are 6,30,96,346
Denominators are 47,72,368,112
The GCF of 6,30,96,346 is 2 .
LCM of 47,72,368,112 is 1089648.
The greatest common factor of 6/47,30/72,96/368,346/112 = [GCF of 6,30,96,346]/[LCM of 47,72,368,112]= 2/1089648
Therefore, the GCF of 6/47,30/72,96/368,346/112 is 2/1089648.
To find the highest common factor of 6,30,96,346, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 346 are 1, 2, 173, 346
The HCF of 6,30,96,346 is 2.
Lets's calculate GCF of 6,30,96,346
2 | 6, 30, 96, 346 |
3, 15, 48, 173 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 346
:1,2,173,346
Greatest Common Factor
We found the factors 6,30,96,346 . The biggest common factor number is the GCF number.
So the greatest common factor 6,30,96,346 is 2.
Lets's calculate LCM of 47,72,368,112
2 | 47, 72, 368, 112 |
2 | 47, 36, 184, 56 |
2 | 47, 18, 92, 28 |
2 | 47, 9, 46, 14 |
47, 9, 23, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 47 x 9 x 23 x 7 = 1089648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1089648
Therefore, the GCF of Fractions 6/47,30/72,96/368,346/112 is 2/1089648
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 47,72,368,112 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(47,72,368,112) = 1
common factors(in case of two or more numbers have common factors) = 128
GCF(47,72,368,112) x common factors =1 x 128 = 128
LCM(47,72,368,112) = ( 47 × 72 × 368 × 112 ) / 128
LCM(47,72,368,112) = 139474944 / 128
LCM(47,72,368,112) = 1089648
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 6,30,96,346?
The HCF of 6,30,96,346 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 6/47, 30/72, 96/368, 346/112?
Answer: GCF of Numerators as per given numbers 6/47, 30/72, 96/368, 346/112 is
GCF of Numerators i.e. for 6,30,96,346 is 2
LCM of denominators i.e. for 47,72,368,112 is 1089648.
Thus, GCF of Fractions is 2/1089648.Finally, GCF of Fractions for 6/47, 30/72, 96/368, 346/112 is 2/1089648.