GCF of 7078/413, 5112/5313
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7078/413, 5112/5313 i.e 2/313467 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7078/413, 5112/5313.
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 7078/413,5112/5313?
Given fractions are 7078/413,5112/5313
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 7078/413,5112/5313, numerators are 7078,5112
Denominators are 413,5313
The GCF of 7078,5112 is 2 .
LCM of 413,5313 is 313467.
The greatest common factor of 7078/413,5112/5313 = [GCF of 7078,5112]/[LCM of 413,5313]= 2/313467
Therefore, the GCF of 7078/413,5112/5313 is 2/313467.
To find the highest common factor of 7078,5112, we have to find the factors of both numbers and list the highest common factor.
The factors of 7078 are 1, 2, 3539, 7078
The factors of 5112 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 71, 72, 142, 213, 284, 426, 568, 639, 852, 1278, 1704, 2556, 5112
The HCF of 7078,5112 is 2.
Lets's calculate GCF of 7078,5112
| 2 | 7078, 5112 |
| 3539, 2556 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7078,5112 By Matching Biggest Common Factor Method
Now, list down the factors of 7078
:1,2,3539,7078
Now, list down the factors of 5112
:1,2,3,4,6,8,9,12,18,24,36,71,72,142,213,284,426,568,639,852,1278,1704,2556,5112
Greatest Common Factor
We found the factors 7078,5112 . The biggest common factor number is the GCF number.
So the greatest common factor 7078,5112 is 2.
Lets's calculate LCM of 413,5313
| 7 | 413, 5313 |
| 59, 759 |
∴ So the LCM of the given numbers is 7 x 59 x 759 = 313467
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/313467
Therefore, the GCF of Fractions 7078/413,5112/5313 is 2/313467
Least Common Multiple of 413,5313 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 413,5313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,5313) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(413,5313) x common factors =7 x 1 = 7
LCM(413,5313) = ( 413 × 5313 ) / 7
LCM(413,5313) = 2194269 / 7
LCM(413,5313) = 313467
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7078/413, 5112/5313
1. What is the HCF of 7078,5112?
The HCF of 7078,5112 is 2
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 7078/413, 5112/5313?
Answer: GCF of Numerators as per given numbers 7078/413, 5112/5313 is
GCF of Numerators i.e. for 7078,5112 is 2
LCM of denominators i.e. for 413,5313 is 313467.
Thus, GCF of Fractions is 2/313467.Finally, GCF of Fractions for 7078/413, 5112/5313 is 2/313467.