GCF of 516/108, 946/192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 516/108, 946/192 i.e 86/1728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/108, 946/192.
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 516/108,946/192?
Given fractions are 516/108,946/192
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 516/108,946/192, numerators are 516,946
Denominators are 108,192
The GCF of 516,946 is 86 .
LCM of 108,192 is 1728.
The greatest common factor of 516/108,946/192 = [GCF of 516,946]/[LCM of 108,192]= 86/1728
Therefore, the GCF of 516/108,946/192 is 86/1728.
To find the highest common factor of 516,946, 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 946 are 1, 2, 11, 22, 43, 86, 473, 946
The HCF of 516,946 is 86.
Lets's calculate GCF of 516,946
| 2 | 516, 946 |
| 43 | 258, 473 |
| 6, 11 |
∴ So the GCF of the given numbers is 2 x 43 = 86
Greatest Common Factor of 516,946 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 946
:1,2,11,22,43,86,473,946
Greatest Common Factor
We found the factors 516,946 . The biggest common factor number is the GCF number.
So the greatest common factor 516,946 is 86.
Lets's calculate LCM of 108,192
| 2 | 108, 192 |
| 2 | 54, 96 |
| 3 | 27, 48 |
| 9, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 9 x 16 = 1728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 86/1728
Therefore, the GCF of Fractions 516/108,946/192 is 86/1728
Least Common Multiple of 108,192 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 108,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,192) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(108,192) x common factors =12 x 1 = 12
LCM(108,192) = ( 108 × 192 ) / 12
LCM(108,192) = 20736 / 12
LCM(108,192) = 1728
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FAQs on GCF of Fractions of 516/108, 946/192
1. What is the HCF of 516,946?
The HCF of 516,946 is 86
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 516/108, 946/192?
Answer: GCF of Numerators as per given numbers 516/108, 946/192 is
GCF of Numerators i.e. for 516,946 is 86
LCM of denominators i.e. for 108,192 is 1728.
Thus, GCF of Fractions is 86/1728.Finally, GCF of Fractions for 516/108, 946/192 is 86/1728.