GCF of 7470/285, 7138/6640
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7470/285, 7138/6640 i.e 166/378480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7470/285, 7138/6640.
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 7470/285,7138/6640?
Given fractions are 7470/285,7138/6640
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 7470/285,7138/6640, numerators are 7470,7138
Denominators are 285,6640
The GCF of 7470,7138 is 166 .
LCM of 285,6640 is 378480.
The greatest common factor of 7470/285,7138/6640 = [GCF of 7470,7138]/[LCM of 285,6640]= 166/378480
Therefore, the GCF of 7470/285,7138/6640 is 166/378480.
To find the highest common factor of 7470,7138, we have to find the factors of both numbers and list the highest common factor.
The factors of 7470 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 83, 90, 166, 249, 415, 498, 747, 830, 1245, 1494, 2490, 3735, 7470
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The HCF of 7470,7138 is 166.
Lets's calculate GCF of 7470,7138
| 2 | 7470, 7138 |
| 83 | 3735, 3569 |
| 45, 43 |
∴ So the GCF of the given numbers is 2 x 83 = 166
Greatest Common Factor of 7470,7138 By Matching Biggest Common Factor Method
Now, list down the factors of 7470
:1,2,3,5,6,9,10,15,18,30,45,83,90,166,249,415,498,747,830,1245,1494,2490,3735,7470
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Greatest Common Factor
We found the factors 7470,7138 . The biggest common factor number is the GCF number.
So the greatest common factor 7470,7138 is 166.
Lets's calculate LCM of 285,6640
| 5 | 285, 6640 |
| 57, 1328 |
∴ So the LCM of the given numbers is 5 x 57 x 1328 = 378480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 166/378480
Therefore, the GCF of Fractions 7470/285,7138/6640 is 166/378480
Least Common Multiple of 285,6640 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 285,6640 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(285,6640) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(285,6640) x common factors =5 x 1 = 5
LCM(285,6640) = ( 285 × 6640 ) / 5
LCM(285,6640) = 1892400 / 5
LCM(285,6640) = 378480
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FAQs on GCF of Fractions of 7470/285, 7138/6640
1. What is the HCF of 7470,7138?
The HCF of 7470,7138 is 166
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 7470/285, 7138/6640?
Answer: GCF of Numerators as per given numbers 7470/285, 7138/6640 is
GCF of Numerators i.e. for 7470,7138 is 166
LCM of denominators i.e. for 285,6640 is 378480.
Thus, GCF of Fractions is 166/378480.Finally, GCF of Fractions for 7470/285, 7138/6640 is 166/378480.