GCF of 760/578, 960/167
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 760/578, 960/167 i.e 40/96526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/578, 960/167.
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 760/578,960/167?
Given fractions are 760/578,960/167
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 760/578,960/167, numerators are 760,960
Denominators are 578,167
The GCF of 760,960 is 40 .
LCM of 578,167 is 96526.
The greatest common factor of 760/578,960/167 = [GCF of 760,960]/[LCM of 578,167]= 40/96526
Therefore, the GCF of 760/578,960/167 is 40/96526.
To find the highest common factor of 760,960, 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 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 760,960 is 40.
Lets's calculate GCF of 760,960
| 2 | 760, 960 |
| 2 | 380, 480 |
| 2 | 190, 240 |
| 5 | 95, 120 |
| 19, 24 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 760,960 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 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 760,960 . The biggest common factor number is the GCF number.
So the greatest common factor 760,960 is 40.
Lets's calculate LCM of 578,167
Given numbers has no common factors except 1. So, there LCM is their product i.e 96526
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/96526
Therefore, the GCF of Fractions 760/578,960/167 is 40/96526
Least Common Multiple of 578,167 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 578,167 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,167) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(578,167) x common factors =1 x 1 = 1
LCM(578,167) = ( 578 × 167 ) / 1
LCM(578,167) = 96526 / 1
LCM(578,167) = 96526
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FAQs on GCF of Fractions of 760/578, 960/167
1. What is the HCF of 760,960?
The HCF of 760,960 is 40
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 760/578, 960/167?
Answer: GCF of Numerators as per given numbers 760/578, 960/167 is
GCF of Numerators i.e. for 760,960 is 40
LCM of denominators i.e. for 578,167 is 96526.
Thus, GCF of Fractions is 40/96526.Finally, GCF of Fractions for 760/578, 960/167 is 40/96526.