GCF of 4065/760, 5709/576
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4065/760, 5709/576 i.e 3/54720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4065/760, 5709/576.
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 4065/760,5709/576?
Given fractions are 4065/760,5709/576
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 4065/760,5709/576, numerators are 4065,5709
Denominators are 760,576
The GCF of 4065,5709 is 3 .
LCM of 760,576 is 54720.
The greatest common factor of 4065/760,5709/576 = [GCF of 4065,5709]/[LCM of 760,576]= 3/54720
Therefore, the GCF of 4065/760,5709/576 is 3/54720.
To find the highest common factor of 4065,5709, we have to find the factors of both numbers and list the highest common factor.
The factors of 4065 are 1, 3, 5, 15, 271, 813, 1355, 4065
The factors of 5709 are 1, 3, 11, 33, 173, 519, 1903, 5709
The HCF of 4065,5709 is 3.
Lets's calculate GCF of 4065,5709
| 3 | 4065, 5709 |
| 1355, 1903 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 4065,5709 By Matching Biggest Common Factor Method
Now, list down the factors of 4065
:1,3,5,15,271,813,1355,4065
Now, list down the factors of 5709
:1,3,11,33,173,519,1903,5709
Greatest Common Factor
We found the factors 4065,5709 . The biggest common factor number is the GCF number.
So the greatest common factor 4065,5709 is 3.
Lets's calculate LCM of 760,576
| 2 | 760, 576 |
| 2 | 380, 288 |
| 2 | 190, 144 |
| 95, 72 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 95 x 72 = 54720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/54720
Therefore, the GCF of Fractions 4065/760,5709/576 is 3/54720
Least Common Multiple of 760,576 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 760,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(760,576) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(760,576) x common factors =8 x 1 = 8
LCM(760,576) = ( 760 × 576 ) / 8
LCM(760,576) = 437760 / 8
LCM(760,576) = 54720
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FAQs on GCF of Fractions of 4065/760, 5709/576
1. What is the HCF of 4065,5709?
The HCF of 4065,5709 is 3
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 4065/760, 5709/576?
Answer: GCF of Numerators as per given numbers 4065/760, 5709/576 is
GCF of Numerators i.e. for 4065,5709 is 3
LCM of denominators i.e. for 760,576 is 54720.
Thus, GCF of Fractions is 3/54720.Finally, GCF of Fractions for 4065/760, 5709/576 is 3/54720.