Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 234/78,562/87,128/102
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 234,562,128
Greatest Common Factor of Numerators i.e. GCF of 234,562,128 is 2 .
LCM of Denominators means LCM of 78,87,102 as per the given fractions.
LCM of 78,87,102 is 38454 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 234,562,128
2 | 234, 562, 128 |
117, 281, 64 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 234
List of positive integer factors of 234 that divides 234 without a remainder.
1,2,3,6,9,13,18,26,39,78,117,234
Factors of 562
List of positive integer factors of 562 that divides 562 without a remainder.
1,2,281,562
Factors of 128
List of positive integer factors of 128 that divides 128 without a remainder.
1,2,4,8,16,32,64,128
Greatest Common Factor
We found the factors 234,562,128 . The biggest common factor number is the GCF number.
So the greatest common factor 234,562,128 is 2.
Lets's calculate LCM of 78,87,102
2 | 78, 87, 102 |
3 | 39, 87, 51 |
13, 29, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 29 x 17 = 38454
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38454
Therefore, the GCF of Fractions 234/78,562/87,128/102 is 2/38454
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 78,87,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,87,102) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(78,87,102) x common factors =3 x 6 = 18
LCM(78,87,102) = ( 78 × 87 × 102 ) / 18
LCM(78,87,102) = 692172 / 18
LCM(78,87,102) = 38454
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 234/78, 562/87, 128/102?
Answer: GCF of Numerators as per given numbers 234/78, 562/87, 128/102 is
GCF of Numerators i.e. for 234,562,128 is 2
LCM of denominators i.e. for 78,87,102 is 38454.
Thus, GCF of Fractions is 2/38454.Finally, GCF of Fractions for 234/78, 562/87, 128/102 is 2/38454.