GCF of 516/381, 351/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 516/381, 351/706 i.e 3/268986 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/381, 351/706.
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 516/381,351/706?
Given fractions are 516/381,351/706
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 516/381,351/706, numerators are 516,351
Denominators are 381,706
The GCF of 516,351 is 3 .
LCM of 381,706 is 268986.
The greatest common factor of 516/381,351/706 = [GCF of 516,351]/[LCM of 381,706]= 3/268986
Therefore, the GCF of 516/381,351/706 is 3/268986.
To find the highest common factor of 516,351, we have to find the factors of both numbers and list the highest common factor.
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351
The HCF of 516,351 is 3.
Lets's calculate GCF of 516,351
| 3 | 516, 351 |
| 172, 117 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 516,351 By Matching Biggest Common Factor Method
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Now, list down the factors of 351
:1,3,9,13,27,39,117,351
Greatest Common Factor
We found the factors 516,351 . The biggest common factor number is the GCF number.
So the greatest common factor 516,351 is 3.
Lets's calculate LCM of 381,706
Given numbers has no common factors except 1. So, there LCM is their product i.e 268986
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/268986
Therefore, the GCF of Fractions 516/381,351/706 is 3/268986
Least Common Multiple of 381,706 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 381,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(381,706) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(381,706) x common factors =1 x 1 = 1
LCM(381,706) = ( 381 × 706 ) / 1
LCM(381,706) = 268986 / 1
LCM(381,706) = 268986
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FAQs on GCF of Fractions of 516/381, 351/706
1. What is the HCF of 516,351?
The HCF of 516,351 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 516/381, 351/706?
Answer: GCF of Numerators as per given numbers 516/381, 351/706 is
GCF of Numerators i.e. for 516,351 is 3
LCM of denominators i.e. for 381,706 is 268986.
Thus, GCF of Fractions is 3/268986.Finally, GCF of Fractions for 516/381, 351/706 is 3/268986.