GCF of 7410/738, 8094/465
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7410/738, 8094/465 i.e 114/114390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7410/738, 8094/465.
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 7410/738,8094/465?
Given fractions are 7410/738,8094/465
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 7410/738,8094/465, numerators are 7410,8094
Denominators are 738,465
The GCF of 7410,8094 is 114 .
LCM of 738,465 is 114390.
The greatest common factor of 7410/738,8094/465 = [GCF of 7410,8094]/[LCM of 738,465]= 114/114390
Therefore, the GCF of 7410/738,8094/465 is 114/114390.
To find the highest common factor of 7410,8094, we have to find the factors of both numbers and list the highest common factor.
The factors of 7410 are 1, 2, 3, 5, 6, 10, 13, 15, 19, 26, 30, 38, 39, 57, 65, 78, 95, 114, 130, 190, 195, 247, 285, 390, 494, 570, 741, 1235, 1482, 2470, 3705, 7410
The factors of 8094 are 1, 2, 3, 6, 19, 38, 57, 71, 114, 142, 213, 426, 1349, 2698, 4047, 8094
The HCF of 7410,8094 is 114.
Lets's calculate GCF of 7410,8094
| 2 | 7410, 8094 |
| 3 | 3705, 4047 |
| 19 | 1235, 1349 |
| 65, 71 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Greatest Common Factor of 7410,8094 By Matching Biggest Common Factor Method
Now, list down the factors of 7410
:1,2,3,5,6,10,13,15,19,26,30,38,39,57,65,78,95,114,130,190,195,247,285,390,494,570,741,1235,1482,2470,3705,7410
Now, list down the factors of 8094
:1,2,3,6,19,38,57,71,114,142,213,426,1349,2698,4047,8094
Greatest Common Factor
We found the factors 7410,8094 . The biggest common factor number is the GCF number.
So the greatest common factor 7410,8094 is 114.
Lets's calculate LCM of 738,465
| 3 | 738, 465 |
| 246, 155 |
∴ So the LCM of the given numbers is 3 x 246 x 155 = 114390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/114390
Therefore, the GCF of Fractions 7410/738,8094/465 is 114/114390
Least Common Multiple of 738,465 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 738,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(738,465) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(738,465) x common factors =3 x 1 = 3
LCM(738,465) = ( 738 × 465 ) / 3
LCM(738,465) = 343170 / 3
LCM(738,465) = 114390
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FAQs on GCF of Fractions of 7410/738, 8094/465
1. What is the HCF of 7410,8094?
The HCF of 7410,8094 is 114
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 7410/738, 8094/465?
Answer: GCF of Numerators as per given numbers 7410/738, 8094/465 is
GCF of Numerators i.e. for 7410,8094 is 114
LCM of denominators i.e. for 738,465 is 114390.
Thus, GCF of Fractions is 114/114390.Finally, GCF of Fractions for 7410/738, 8094/465 is 114/114390.