Use our free GCF of Fractions Calculator tool to compute the GCF of 31/545, 42/621, 196/684 i.e 1/25721820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/545, 42/621, 196/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/545,42/621,196/684
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 31/545,42/621,196/684, numerators are 31,42,196
Denominators are 545,621,684
The GCF of 31,42,196 is 1 .
LCM of 545,621,684 is 25721820.
The greatest common factor of 31/545,42/621,196/684 = [GCF of 31,42,196]/[LCM of 545,621,684]= 1/25721820
Therefore, the GCF of 31/545,42/621,196/684 is 1/25721820.
To find the highest common factor of 31,42,196, we have to find the factors of both numbers and list the highest common factor.
The factors of 31 are 1, 31
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196
The HCF of 31,42,196 is 1.
Lets's calculate GCF of 31,42,196
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 31
:1,31
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 196
:1,2,4,7,14,28,49,98,196
Greatest Common Factor
We found the factors 31,42,196 . The biggest common factor number is the GCF number.
So the greatest common factor 31,42,196 is 1.
Lets's calculate LCM of 545,621,684
3 | 545, 621, 684 |
3 | 545, 207, 228 |
545, 69, 76 |
∴ So the LCM of the given numbers is 3 x 3 x 545 x 69 x 76 = 25721820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25721820
Therefore, the GCF of Fractions 31/545,42/621,196/684 is 1/25721820
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 545,621,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(545,621,684) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(545,621,684) x common factors =1 x 9 = 9
LCM(545,621,684) = ( 545 × 621 × 684 ) / 9
LCM(545,621,684) = 231496380 / 9
LCM(545,621,684) = 25721820
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 31,42,196?
The HCF of 31,42,196 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 31/545, 42/621, 196/684?
Answer: GCF of Numerators as per given numbers 31/545, 42/621, 196/684 is
GCF of Numerators i.e. for 31,42,196 is 1
LCM of denominators i.e. for 545,621,684 is 25721820.
Thus, GCF of Fractions is 1/25721820.Finally, GCF of Fractions for 31/545, 42/621, 196/684 is 1/25721820.