Use our free GCF of Fractions Calculator tool to compute the GCF of 14/206, 39/837, 784/829 i.e 1/142937838 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/206, 39/837, 784/829.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/206,39/837,784/829
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 14/206,39/837,784/829, numerators are 14,39,784
Denominators are 206,837,829
The GCF of 14,39,784 is 1 .
LCM of 206,837,829 is 142937838.
The greatest common factor of 14/206,39/837,784/829 = [GCF of 14,39,784]/[LCM of 206,837,829]= 1/142937838
Therefore, the GCF of 14/206,39/837,784/829 is 1/142937838.
To find the highest common factor of 14,39,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 39 are 1, 3, 13, 39
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 14,39,784 is 1.
Lets's calculate GCF of 14,39,784
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 14,39,784 . The biggest common factor number is the GCF number.
So the greatest common factor 14,39,784 is 1.
Lets's calculate LCM of 206,837,829
Given numbers has no common factors except 1. So, there LCM is their product i.e 142937838
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/142937838
Therefore, the GCF of Fractions 14/206,39/837,784/829 is 1/142937838
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 206,837,829 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,837,829) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(206,837,829) x common factors =1 x 1 = 1
LCM(206,837,829) = ( 206 × 837 × 829 ) / 1
LCM(206,837,829) = 142937838 / 1
LCM(206,837,829) = 142937838
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,39,784?
The HCF of 14,39,784 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 14/206, 39/837, 784/829?
Answer: GCF of Numerators as per given numbers 14/206, 39/837, 784/829 is
GCF of Numerators i.e. for 14,39,784 is 1
LCM of denominators i.e. for 206,837,829 is 142937838.
Thus, GCF of Fractions is 1/142937838.Finally, GCF of Fractions for 14/206, 39/837, 784/829 is 1/142937838.