GCF of 760/378, 735/320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 760/378, 735/320 i.e 5/60480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/378, 735/320.
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 760/378,735/320?
Given fractions are 760/378,735/320
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 760/378,735/320, numerators are 760,735
Denominators are 378,320
The GCF of 760,735 is 5 .
LCM of 378,320 is 60480.
The greatest common factor of 760/378,735/320 = [GCF of 760,735]/[LCM of 378,320]= 5/60480
Therefore, the GCF of 760/378,735/320 is 5/60480.
To find the highest common factor of 760,735, we have to find the factors of both numbers and list the highest common factor.
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The HCF of 760,735 is 5.
Lets's calculate GCF of 760,735
| 5 | 760, 735 |
| 152, 147 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 760,735 By Matching Biggest Common Factor Method
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 760,735 . The biggest common factor number is the GCF number.
So the greatest common factor 760,735 is 5.
Lets's calculate LCM of 378,320
| 2 | 378, 320 |
| 189, 160 |
∴ So the LCM of the given numbers is 2 x 189 x 160 = 60480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/60480
Therefore, the GCF of Fractions 760/378,735/320 is 5/60480
Least Common Multiple of 378,320 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 378,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,320) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(378,320) x common factors =2 x 1 = 2
LCM(378,320) = ( 378 × 320 ) / 2
LCM(378,320) = 120960 / 2
LCM(378,320) = 60480
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FAQs on GCF of Fractions of 760/378, 735/320
1. What is the HCF of 760,735?
The HCF of 760,735 is 5
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 760/378, 735/320?
Answer: GCF of Numerators as per given numbers 760/378, 735/320 is
GCF of Numerators i.e. for 760,735 is 5
LCM of denominators i.e. for 378,320 is 60480.
Thus, GCF of Fractions is 5/60480.Finally, GCF of Fractions for 760/378, 735/320 is 5/60480.