GCF of 7434/413, 8080/7198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7434/413, 8080/7198 i.e 2/50386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7434/413, 8080/7198.
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 7434/413,8080/7198?
Given fractions are 7434/413,8080/7198
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 7434/413,8080/7198, numerators are 7434,8080
Denominators are 413,7198
The GCF of 7434,8080 is 2 .
LCM of 413,7198 is 50386.
The greatest common factor of 7434/413,8080/7198 = [GCF of 7434,8080]/[LCM of 413,7198]= 2/50386
Therefore, the GCF of 7434/413,8080/7198 is 2/50386.
To find the highest common factor of 7434,8080, we have to find the factors of both numbers and list the highest common factor.
The factors of 7434 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 59, 63, 118, 126, 177, 354, 413, 531, 826, 1062, 1239, 2478, 3717, 7434
The factors of 8080 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 101, 202, 404, 505, 808, 1010, 1616, 2020, 4040, 8080
The HCF of 7434,8080 is 2.
Lets's calculate GCF of 7434,8080
| 2 | 7434, 8080 |
| 3717, 4040 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7434,8080 By Matching Biggest Common Factor Method
Now, list down the factors of 7434
:1,2,3,6,7,9,14,18,21,42,59,63,118,126,177,354,413,531,826,1062,1239,2478,3717,7434
Now, list down the factors of 8080
:1,2,4,5,8,10,16,20,40,80,101,202,404,505,808,1010,1616,2020,4040,8080
Greatest Common Factor
We found the factors 7434,8080 . The biggest common factor number is the GCF number.
So the greatest common factor 7434,8080 is 2.
Lets's calculate LCM of 413,7198
| 59 | 413, 7198 |
| 7, 122 |
∴ So the LCM of the given numbers is 59 x 7 x 122 = 50386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/50386
Therefore, the GCF of Fractions 7434/413,8080/7198 is 2/50386
Least Common Multiple of 413,7198 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 413,7198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,7198) = 59
common factors(in case of two or more numbers have common factors) = 1
GCF(413,7198) x common factors =59 x 1 = 59
LCM(413,7198) = ( 413 × 7198 ) / 59
LCM(413,7198) = 2972774 / 59
LCM(413,7198) = 50386
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FAQs on GCF of Fractions of 7434/413, 8080/7198
1. What is the HCF of 7434,8080?
The HCF of 7434,8080 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 7434/413, 8080/7198?
Answer: GCF of Numerators as per given numbers 7434/413, 8080/7198 is
GCF of Numerators i.e. for 7434,8080 is 2
LCM of denominators i.e. for 413,7198 is 50386.
Thus, GCF of Fractions is 2/50386.Finally, GCF of Fractions for 7434/413, 8080/7198 is 2/50386.