Use our free GCF of Fractions Calculator tool to compute the GCF of 39/214, 49/641, 869/414 i.e 1/28395018 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/214, 49/641, 869/414.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 39/214,49/641,869/414
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 39/214,49/641,869/414, numerators are 39,49,869
Denominators are 214,641,414
The GCF of 39,49,869 is 1 .
LCM of 214,641,414 is 28395018.
The greatest common factor of 39/214,49/641,869/414 = [GCF of 39,49,869]/[LCM of 214,641,414]= 1/28395018
Therefore, the GCF of 39/214,49/641,869/414 is 1/28395018.
To find the highest common factor of 39,49,869, we have to find the factors of both numbers and list the highest common factor.
The factors of 39 are 1, 3, 13, 39
The factors of 49 are 1, 7, 49
The factors of 869 are 1, 11, 79, 869
The HCF of 39,49,869 is 1.
Lets's calculate GCF of 39,49,869
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 869
:1,11,79,869
Greatest Common Factor
We found the factors 39,49,869 . The biggest common factor number is the GCF number.
So the greatest common factor 39,49,869 is 1.
Lets's calculate LCM of 214,641,414
2 | 214, 641, 414 |
107, 641, 207 |
∴ So the LCM of the given numbers is 2 x 107 x 641 x 207 = 28395018
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28395018
Therefore, the GCF of Fractions 39/214,49/641,869/414 is 1/28395018
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 214,641,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,641,414) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(214,641,414) x common factors =1 x 2 = 2
LCM(214,641,414) = ( 214 × 641 × 414 ) / 2
LCM(214,641,414) = 56790036 / 2
LCM(214,641,414) = 28395018
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 39,49,869?
The HCF of 39,49,869 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 39/214, 49/641, 869/414?
Answer: GCF of Numerators as per given numbers 39/214, 49/641, 869/414 is
GCF of Numerators i.e. for 39,49,869 is 1
LCM of denominators i.e. for 214,641,414 is 28395018.
Thus, GCF of Fractions is 1/28395018.Finally, GCF of Fractions for 39/214, 49/641, 869/414 is 1/28395018.