GCF of 516/407, 658/504
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 516/407, 658/504 i.e 2/205128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/407, 658/504.
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 516/407,658/504?
Given fractions are 516/407,658/504
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 516/407,658/504, numerators are 516,658
Denominators are 407,504
The GCF of 516,658 is 2 .
LCM of 407,504 is 205128.
The greatest common factor of 516/407,658/504 = [GCF of 516,658]/[LCM of 407,504]= 2/205128
Therefore, the GCF of 516/407,658/504 is 2/205128.
To find the highest common factor of 516,658, 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 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 516,658 is 2.
Lets's calculate GCF of 516,658
| 2 | 516, 658 |
| 258, 329 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 516,658 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 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 516,658 . The biggest common factor number is the GCF number.
So the greatest common factor 516,658 is 2.
Lets's calculate LCM of 407,504
Given numbers has no common factors except 1. So, there LCM is their product i.e 205128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/205128
Therefore, the GCF of Fractions 516/407,658/504 is 2/205128
Least Common Multiple of 407,504 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 407,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(407,504) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(407,504) x common factors =1 x 1 = 1
LCM(407,504) = ( 407 × 504 ) / 1
LCM(407,504) = 205128 / 1
LCM(407,504) = 205128
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FAQs on GCF of Fractions of 516/407, 658/504
1. What is the HCF of 516,658?
The HCF of 516,658 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 516/407, 658/504?
Answer: GCF of Numerators as per given numbers 516/407, 658/504 is
GCF of Numerators i.e. for 516,658 is 2
LCM of denominators i.e. for 407,504 is 205128.
Thus, GCF of Fractions is 2/205128.Finally, GCF of Fractions for 516/407, 658/504 is 2/205128.