Use our free GCF of Fractions Calculator tool to compute the GCF of 142/840, 684/346 i.e 2/145320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/840, 684/346.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 142/840,684/346
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 142/840,684/346, numerators are 142,684
Denominators are 840,346
The GCF of 142,684 is 2 .
LCM of 840,346 is 145320.
The greatest common factor of 142/840,684/346 = [GCF of 142,684]/[LCM of 840,346]= 2/145320
Therefore, the GCF of 142/840,684/346 is 2/145320.
To find the highest common factor of 142,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 142 are 1, 2, 71, 142
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 142,684 is 2.
Lets's calculate GCF of 142,684
2 | 142, 684 |
71, 342 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 142
:1,2,71,142
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 142,684 . The biggest common factor number is the GCF number.
So the greatest common factor 142,684 is 2.
Lets's calculate LCM of 840,346
2 | 840, 346 |
420, 173 |
∴ So the LCM of the given numbers is 2 x 420 x 173 = 145320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/145320
Therefore, the GCF of Fractions 142/840,684/346 is 2/145320
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 840,346 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,346) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(840,346) x common factors =2 x 1 = 2
LCM(840,346) = ( 840 × 346 ) / 2
LCM(840,346) = 290640 / 2
LCM(840,346) = 145320
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 142,684?
The HCF of 142,684 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 142/840, 684/346?
Answer: GCF of Numerators as per given numbers 142/840, 684/346 is
GCF of Numerators i.e. for 142,684 is 2
LCM of denominators i.e. for 840,346 is 145320.
Thus, GCF of Fractions is 2/145320.Finally, GCF of Fractions for 142/840, 684/346 is 2/145320.