GCF of 7740/723, 7310/7423
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7740/723, 7310/7423 i.e 430/5366829 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7740/723, 7310/7423.
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 7740/723,7310/7423?
Given fractions are 7740/723,7310/7423
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 7740/723,7310/7423, numerators are 7740,7310
Denominators are 723,7423
The GCF of 7740,7310 is 430 .
LCM of 723,7423 is 5366829.
The greatest common factor of 7740/723,7310/7423 = [GCF of 7740,7310]/[LCM of 723,7423]= 430/5366829
Therefore, the GCF of 7740/723,7310/7423 is 430/5366829.
To find the highest common factor of 7740,7310, we have to find the factors of both numbers and list the highest common factor.
The factors of 7740 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740
The factors of 7310 are 1, 2, 5, 10, 17, 34, 43, 85, 86, 170, 215, 430, 731, 1462, 3655, 7310
The HCF of 7740,7310 is 430.
Lets's calculate GCF of 7740,7310
| 2 | 7740, 7310 |
| 5 | 3870, 3655 |
| 43 | 774, 731 |
| 18, 17 |
∴ So the GCF of the given numbers is 2 x 5 x 43 = 430
Greatest Common Factor of 7740,7310 By Matching Biggest Common Factor Method
Now, list down the factors of 7740
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,43,45,60,86,90,129,172,180,215,258,387,430,516,645,774,860,1290,1548,1935,2580,3870,7740
Now, list down the factors of 7310
:1,2,5,10,17,34,43,85,86,170,215,430,731,1462,3655,7310
Greatest Common Factor
We found the factors 7740,7310 . The biggest common factor number is the GCF number.
So the greatest common factor 7740,7310 is 430.
Lets's calculate LCM of 723,7423
Given numbers has no common factors except 1. So, there LCM is their product i.e 5366829
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 430/5366829
Therefore, the GCF of Fractions 7740/723,7310/7423 is 430/5366829
Least Common Multiple of 723,7423 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 723,7423 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,7423) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(723,7423) x common factors =1 x 1 = 1
LCM(723,7423) = ( 723 × 7423 ) / 1
LCM(723,7423) = 5366829 / 1
LCM(723,7423) = 5366829
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FAQs on GCF of Fractions of 7740/723, 7310/7423
1. What is the HCF of 7740,7310?
The HCF of 7740,7310 is 430
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 7740/723, 7310/7423?
Answer: GCF of Numerators as per given numbers 7740/723, 7310/7423 is
GCF of Numerators i.e. for 7740,7310 is 430
LCM of denominators i.e. for 723,7423 is 5366829.
Thus, GCF of Fractions is 430/5366829.Finally, GCF of Fractions for 7740/723, 7310/7423 is 430/5366829.