Use our free GCF of Fractions Calculator tool to compute the GCF of 156/49, 858/7314 i.e 78/358386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/49, 858/7314.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 156/49,858/7314
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 156/49,858/7314, numerators are 156,858
Denominators are 49,7314
The GCF of 156,858 is 78 .
LCM of 49,7314 is 358386.
The greatest common factor of 156/49,858/7314 = [GCF of 156,858]/[LCM of 49,7314]= 78/358386
Therefore, the GCF of 156/49,858/7314 is 78/358386.
To find the highest common factor of 156,858, we have to find the factors of both numbers and list the highest common factor.
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The HCF of 156,858 is 78.
Lets's calculate GCF of 156,858
2 | 156, 858 |
3 | 78, 429 |
13 | 26, 143 |
2, 11 |
∴ So the GCF of the given numbers is 2 x 3 x 13 = 78
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Greatest Common Factor
We found the factors 156,858 . The biggest common factor number is the GCF number.
So the greatest common factor 156,858 is 78.
Lets's calculate LCM of 49,7314
Given numbers has no common factors except 1. So, there LCM is their product i.e 358386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 78/358386
Therefore, the GCF of Fractions 156/49,858/7314 is 78/358386
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 49,7314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,7314) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,7314) x common factors =1 x 1 = 1
LCM(49,7314) = ( 49 × 7314 ) / 1
LCM(49,7314) = 358386 / 1
LCM(49,7314) = 358386
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 156,858?
The HCF of 156,858 is 78
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 156/49, 858/7314?
Answer: GCF of Numerators as per given numbers 156/49, 858/7314 is
GCF of Numerators i.e. for 156,858 is 78
LCM of denominators i.e. for 49,7314 is 358386.
Thus, GCF of Fractions is 78/358386.Finally, GCF of Fractions for 156/49, 858/7314 is 78/358386.