GCF of 8002/576, 8077/540
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8002/576, 8077/540 i.e 1/8640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8002/576, 8077/540.
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 8002/576,8077/540?
Given fractions are 8002/576,8077/540
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 8002/576,8077/540, numerators are 8002,8077
Denominators are 576,540
The GCF of 8002,8077 is 1 .
LCM of 576,540 is 8640.
The greatest common factor of 8002/576,8077/540 = [GCF of 8002,8077]/[LCM of 576,540]= 1/8640
Therefore, the GCF of 8002/576,8077/540 is 1/8640.
To find the highest common factor of 8002,8077, we have to find the factors of both numbers and list the highest common factor.
The factors of 8002 are 1, 2, 4001, 8002
The factors of 8077 are 1, 41, 197, 8077
The HCF of 8002,8077 is 1.
Lets's calculate GCF of 8002,8077
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8002,8077 By Matching Biggest Common Factor Method
Now, list down the factors of 8002
:1,2,4001,8002
Now, list down the factors of 8077
:1,41,197,8077
Greatest Common Factor
We found the factors 8002,8077 . The biggest common factor number is the GCF number.
So the greatest common factor 8002,8077 is 1.
Lets's calculate LCM of 576,540
| 2 | 576, 540 |
| 2 | 288, 270 |
| 3 | 144, 135 |
| 3 | 48, 45 |
| 16, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 16 x 15 = 8640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8640
Therefore, the GCF of Fractions 8002/576,8077/540 is 1/8640
Least Common Multiple of 576,540 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 576,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,540) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(576,540) x common factors =36 x 1 = 36
LCM(576,540) = ( 576 × 540 ) / 36
LCM(576,540) = 311040 / 36
LCM(576,540) = 8640
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FAQs on GCF of Fractions of 8002/576, 8077/540
1. What is the HCF of 8002,8077?
The HCF of 8002,8077 is 1
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 8002/576, 8077/540?
Answer: GCF of Numerators as per given numbers 8002/576, 8077/540 is
GCF of Numerators i.e. for 8002,8077 is 1
LCM of denominators i.e. for 576,540 is 8640.
Thus, GCF of Fractions is 1/8640.Finally, GCF of Fractions for 8002/576, 8077/540 is 1/8640.