GCF of 407/188, 7854/310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 407/188, 7854/310 i.e 11/29140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/188, 7854/310.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 407/188,7854/310?
Given fractions are 407/188,7854/310
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 407/188,7854/310, numerators are 407,7854
Denominators are 188,310
The GCF of 407,7854 is 11 .
LCM of 188,310 is 29140.
The greatest common factor of 407/188,7854/310 = [GCF of 407,7854]/[LCM of 188,310]= 11/29140
Therefore, the GCF of 407/188,7854/310 is 11/29140.
To find the highest common factor of 407,7854, we have to find the factors of both numbers and list the highest common factor.
The factors of 407 are 1, 11, 37, 407
The factors of 7854 are 1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 51, 66, 77, 102, 119, 154, 187, 231, 238, 357, 374, 462, 561, 714, 1122, 1309, 2618, 3927, 7854
The HCF of 407,7854 is 11.
Lets's calculate GCF of 407,7854
| 11 | 407, 7854 |
| 37, 714 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 407,7854 By Matching Biggest Common Factor Method
Now, list down the factors of 407
:1,11,37,407
Now, list down the factors of 7854
:1,2,3,6,7,11,14,17,21,22,33,34,42,51,66,77,102,119,154,187,231,238,357,374,462,561,714,1122,1309,2618,3927,7854
Greatest Common Factor
We found the factors 407,7854 . The biggest common factor number is the GCF number.
So the greatest common factor 407,7854 is 11.
Lets's calculate LCM of 188,310
| 2 | 188, 310 |
| 94, 155 |
∴ So the LCM of the given numbers is 2 x 94 x 155 = 29140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/29140
Therefore, the GCF of Fractions 407/188,7854/310 is 11/29140
Least Common Multiple of 188,310 with GCF Formula
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 188,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,310) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(188,310) x common factors =2 x 1 = 2
LCM(188,310) = ( 188 × 310 ) / 2
LCM(188,310) = 58280 / 2
LCM(188,310) = 29140
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 407/188, 7854/310
1. What is the HCF of 407,7854?
The HCF of 407,7854 is 11
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 407/188, 7854/310?
Answer: GCF of Numerators as per given numbers 407/188, 7854/310 is
GCF of Numerators i.e. for 407,7854 is 11
LCM of denominators i.e. for 188,310 is 29140.
Thus, GCF of Fractions is 11/29140.Finally, GCF of Fractions for 407/188, 7854/310 is 11/29140.