GCF of 14/764, 64/470, 309/497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/764, 64/470, 309/497 i.e 1/89231380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/764, 64/470, 309/497.
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 14/764,64/470,309/497?
Given fractions are 14/764,64/470,309/497
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 14/764,64/470,309/497, numerators are 14,64,309
Denominators are 764,470,497
The GCF of 14,64,309 is 1 .
LCM of 764,470,497 is 89231380.
The greatest common factor of 14/764,64/470,309/497 = [GCF of 14,64,309]/[LCM of 764,470,497]= 1/89231380
Therefore, the GCF of 14/764,64/470,309/497 is 1/89231380.
To find the highest common factor of 14,64,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 309 are 1, 3, 103, 309
The HCF of 14,64,309 is 1.
Lets's calculate GCF of 14,64,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,64,309 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 14,64,309 . The biggest common factor number is the GCF number.
So the greatest common factor 14,64,309 is 1.
Lets's calculate LCM of 764,470,497
| 2 | 764, 470, 497 |
| 382, 235, 497 |
∴ So the LCM of the given numbers is 2 x 382 x 235 x 497 = 89231380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/89231380
Therefore, the GCF of Fractions 14/764,64/470,309/497 is 1/89231380
Least Common Multiple of 764,470,497 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 764,470,497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(764,470,497) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(764,470,497) x common factors =1 x 2 = 2
LCM(764,470,497) = ( 764 × 470 × 497 ) / 2
LCM(764,470,497) = 178462760 / 2
LCM(764,470,497) = 89231380
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FAQs on GCF of Fractions of 14/764, 64/470, 309/497
1. What is the HCF of 14,64,309?
The HCF of 14,64,309 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 14/764, 64/470, 309/497?
Answer: GCF of Numerators as per given numbers 14/764, 64/470, 309/497 is
GCF of Numerators i.e. for 14,64,309 is 1
LCM of denominators i.e. for 764,470,497 is 89231380.
Thus, GCF of Fractions is 1/89231380.Finally, GCF of Fractions for 14/764, 64/470, 309/497 is 1/89231380.