GCF of 34/86, 760/12, 314/453
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/86, 760/12, 314/453 i.e 2/77916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/86, 760/12, 314/453.
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 34/86,760/12,314/453?
Given fractions are 34/86,760/12,314/453
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 34/86,760/12,314/453, numerators are 34,760,314
Denominators are 86,12,453
The GCF of 34,760,314 is 2 .
LCM of 86,12,453 is 77916.
The greatest common factor of 34/86,760/12,314/453 = [GCF of 34,760,314]/[LCM of 86,12,453]= 2/77916
Therefore, the GCF of 34/86,760/12,314/453 is 2/77916.
To find the highest common factor of 34,760,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 314 are 1, 2, 157, 314
The HCF of 34,760,314 is 2.
Lets's calculate GCF of 34,760,314
| 2 | 34, 760, 314 |
| 17, 380, 157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,760,314 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
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 314
:1,2,157,314
Greatest Common Factor
We found the factors 34,760,314 . The biggest common factor number is the GCF number.
So the greatest common factor 34,760,314 is 2.
Lets's calculate LCM of 86,12,453
| 2 | 86, 12, 453 |
| 3 | 43, 6, 453 |
| 43, 2, 151 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 2 x 151 = 77916
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/77916
Therefore, the GCF of Fractions 34/86,760/12,314/453 is 2/77916
Least Common Multiple of 86,12,453 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 86,12,453 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,12,453) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(86,12,453) x common factors =1 x 6 = 6
LCM(86,12,453) = ( 86 × 12 × 453 ) / 6
LCM(86,12,453) = 467496 / 6
LCM(86,12,453) = 77916
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FAQs on GCF of Fractions of 34/86, 760/12, 314/453
1. What is the HCF of 34,760,314?
The HCF of 34,760,314 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 34/86, 760/12, 314/453?
Answer: GCF of Numerators as per given numbers 34/86, 760/12, 314/453 is
GCF of Numerators i.e. for 34,760,314 is 2
LCM of denominators i.e. for 86,12,453 is 77916.
Thus, GCF of Fractions is 2/77916.Finally, GCF of Fractions for 34/86, 760/12, 314/453 is 2/77916.