GCF of 6/65, 52/73, 64/292, 414/131
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/65, 52/73, 64/292, 414/131 i.e 2/2486380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/65, 52/73, 64/292, 414/131.
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 6/65,52/73,64/292,414/131?
Given fractions are 6/65,52/73,64/292,414/131
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 6/65,52/73,64/292,414/131, numerators are 6,52,64,414
Denominators are 65,73,292,131
The GCF of 6,52,64,414 is 2 .
LCM of 65,73,292,131 is 2486380.
The greatest common factor of 6/65,52/73,64/292,414/131 = [GCF of 6,52,64,414]/[LCM of 65,73,292,131]= 2/2486380
Therefore, the GCF of 6/65,52/73,64/292,414/131 is 2/2486380.
To find the highest common factor of 6,52,64,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 6,52,64,414 is 2.
Lets's calculate GCF of 6,52,64,414
| 2 | 6, 52, 64, 414 |
| 3, 26, 32, 207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6,52,64,414 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 6,52,64,414 . The biggest common factor number is the GCF number.
So the greatest common factor 6,52,64,414 is 2.
Lets's calculate LCM of 65,73,292,131
| 73 | 65, 73, 292, 131 |
| 65, 1, 4, 131 |
∴ So the LCM of the given numbers is 73 x 65 x 1 x 4 x 131 = 2486380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2486380
Therefore, the GCF of Fractions 6/65,52/73,64/292,414/131 is 2/2486380
Least Common Multiple of 65,73,292,131 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 65,73,292,131 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,73,292,131) = 1
common factors(in case of two or more numbers have common factors) = 73
GCF(65,73,292,131) x common factors =1 x 73 = 73
LCM(65,73,292,131) = ( 65 × 73 × 292 × 131 ) / 73
LCM(65,73,292,131) = 181505740 / 73
LCM(65,73,292,131) = 2486380
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6/65, 52/73, 64/292, 414/131
1. What is the HCF of 6,52,64,414?
The HCF of 6,52,64,414 is 2
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 6/65, 52/73, 64/292, 414/131?
Answer: GCF of Numerators as per given numbers 6/65, 52/73, 64/292, 414/131 is
GCF of Numerators i.e. for 6,52,64,414 is 2
LCM of denominators i.e. for 65,73,292,131 is 2486380.
Thus, GCF of Fractions is 2/2486380.Finally, GCF of Fractions for 6/65, 52/73, 64/292, 414/131 is 2/2486380.