Use our free GCF of Fractions Calculator tool to compute the GCF of 293/342, 840/174 i.e 1/9918 easily. The following is the detailed procedure to determine the greatest common factor of fractions 293/342, 840/174.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 293/342,840/174
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 293/342,840/174, numerators are 293,840
Denominators are 342,174
The GCF of 293,840 is 1 .
LCM of 342,174 is 9918.
The greatest common factor of 293/342,840/174 = [GCF of 293,840]/[LCM of 342,174]= 1/9918
Therefore, the GCF of 293/342,840/174 is 1/9918.
To find the highest common factor of 293,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 293 are 1, 293
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 293,840 is 1.
Lets's calculate GCF of 293,840
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 293
:1,293
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 293,840 . The biggest common factor number is the GCF number.
So the greatest common factor 293,840 is 1.
Lets's calculate LCM of 342,174
2 | 342, 174 |
3 | 171, 87 |
57, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 57 x 29 = 9918
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9918
Therefore, the GCF of Fractions 293/342,840/174 is 1/9918
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 342,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,174) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(342,174) x common factors =6 x 1 = 6
LCM(342,174) = ( 342 × 174 ) / 6
LCM(342,174) = 59508 / 6
LCM(342,174) = 9918
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 293,840?
The HCF of 293,840 is 1
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 293/342, 840/174?
Answer: GCF of Numerators as per given numbers 293/342, 840/174 is
GCF of Numerators i.e. for 293,840 is 1
LCM of denominators i.e. for 342,174 is 9918.
Thus, GCF of Fractions is 1/9918.Finally, GCF of Fractions for 293/342, 840/174 is 1/9918.