GCF of 7470/638, 8130/422
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7470/638, 8130/422 i.e 30/134618 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7470/638, 8130/422.
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 7470/638,8130/422?
Given fractions are 7470/638,8130/422
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 7470/638,8130/422, numerators are 7470,8130
Denominators are 638,422
The GCF of 7470,8130 is 30 .
LCM of 638,422 is 134618.
The greatest common factor of 7470/638,8130/422 = [GCF of 7470,8130]/[LCM of 638,422]= 30/134618
Therefore, the GCF of 7470/638,8130/422 is 30/134618.
To find the highest common factor of 7470,8130, 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 8130 are 1, 2, 3, 5, 6, 10, 15, 30, 271, 542, 813, 1355, 1626, 2710, 4065, 8130
The HCF of 7470,8130 is 30.
Lets's calculate GCF of 7470,8130
| 2 | 7470, 8130 |
| 3 | 3735, 4065 |
| 5 | 1245, 1355 |
| 249, 271 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 7470,8130 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 8130
:1,2,3,5,6,10,15,30,271,542,813,1355,1626,2710,4065,8130
Greatest Common Factor
We found the factors 7470,8130 . The biggest common factor number is the GCF number.
So the greatest common factor 7470,8130 is 30.
Lets's calculate LCM of 638,422
| 2 | 638, 422 |
| 319, 211 |
∴ So the LCM of the given numbers is 2 x 319 x 211 = 134618
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/134618
Therefore, the GCF of Fractions 7470/638,8130/422 is 30/134618
Least Common Multiple of 638,422 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 638,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(638,422) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(638,422) x common factors =2 x 1 = 2
LCM(638,422) = ( 638 × 422 ) / 2
LCM(638,422) = 269236 / 2
LCM(638,422) = 134618
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FAQs on GCF of Fractions of 7470/638, 8130/422
1. What is the HCF of 7470,8130?
The HCF of 7470,8130 is 30
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 7470/638, 8130/422?
Answer: GCF of Numerators as per given numbers 7470/638, 8130/422 is
GCF of Numerators i.e. for 7470,8130 is 30
LCM of denominators i.e. for 638,422 is 134618.
Thus, GCF of Fractions is 30/134618.Finally, GCF of Fractions for 7470/638, 8130/422 is 30/134618.