GCF of 915/428, 7830/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 915/428, 7830/749 i.e 15/2996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 915/428, 7830/749.
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 915/428,7830/749?
Given fractions are 915/428,7830/749
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 915/428,7830/749, numerators are 915,7830
Denominators are 428,749
The GCF of 915,7830 is 15 .
LCM of 428,749 is 2996.
The greatest common factor of 915/428,7830/749 = [GCF of 915,7830]/[LCM of 428,749]= 15/2996
Therefore, the GCF of 915/428,7830/749 is 15/2996.
To find the highest common factor of 915,7830, we have to find the factors of both numbers and list the highest common factor.
The factors of 915 are 1, 3, 5, 15, 61, 183, 305, 915
The factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830
The HCF of 915,7830 is 15.
Lets's calculate GCF of 915,7830
| 3 | 915, 7830 |
| 5 | 305, 2610 |
| 61, 522 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 915,7830 By Matching Biggest Common Factor Method
Now, list down the factors of 915
:1,3,5,15,61,183,305,915
Now, list down the factors of 7830
:1,2,3,5,6,9,10,15,18,27,29,30,45,54,58,87,90,135,145,174,261,270,290,435,522,783,870,1305,1566,2610,3915,7830
Greatest Common Factor
We found the factors 915,7830 . The biggest common factor number is the GCF number.
So the greatest common factor 915,7830 is 15.
Lets's calculate LCM of 428,749
| 107 | 428, 749 |
| 4, 7 |
∴ So the LCM of the given numbers is 107 x 4 x 7 = 2996
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/2996
Therefore, the GCF of Fractions 915/428,7830/749 is 15/2996
Least Common Multiple of 428,749 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 428,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(428,749) = 107
common factors(in case of two or more numbers have common factors) = 1
GCF(428,749) x common factors =107 x 1 = 107
LCM(428,749) = ( 428 × 749 ) / 107
LCM(428,749) = 320572 / 107
LCM(428,749) = 2996
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FAQs on GCF of Fractions of 915/428, 7830/749
1. What is the HCF of 915,7830?
The HCF of 915,7830 is 15
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 915/428, 7830/749?
Answer: GCF of Numerators as per given numbers 915/428, 7830/749 is
GCF of Numerators i.e. for 915,7830 is 15
LCM of denominators i.e. for 428,749 is 2996.
Thus, GCF of Fractions is 15/2996.Finally, GCF of Fractions for 915/428, 7830/749 is 15/2996.