GCF of 546/715, 458/574
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 546/715, 458/574 i.e 2/410410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/715, 458/574.
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 546/715,458/574?
Given fractions are 546/715,458/574
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 546/715,458/574, numerators are 546,458
Denominators are 715,574
The GCF of 546,458 is 2 .
LCM of 715,574 is 410410.
The greatest common factor of 546/715,458/574 = [GCF of 546,458]/[LCM of 715,574]= 2/410410
Therefore, the GCF of 546/715,458/574 is 2/410410.
To find the highest common factor of 546,458, we have to find the factors of both numbers and list the highest common factor.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 458 are 1, 2, 229, 458
The HCF of 546,458 is 2.
Lets's calculate GCF of 546,458
| 2 | 546, 458 |
| 273, 229 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 546,458 By Matching Biggest Common Factor Method
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 458
:1,2,229,458
Greatest Common Factor
We found the factors 546,458 . The biggest common factor number is the GCF number.
So the greatest common factor 546,458 is 2.
Lets's calculate LCM of 715,574
Given numbers has no common factors except 1. So, there LCM is their product i.e 410410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/410410
Therefore, the GCF of Fractions 546/715,458/574 is 2/410410
Least Common Multiple of 715,574 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 715,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(715,574) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(715,574) x common factors =1 x 1 = 1
LCM(715,574) = ( 715 × 574 ) / 1
LCM(715,574) = 410410 / 1
LCM(715,574) = 410410
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 546/715, 458/574
1. What is the HCF of 546,458?
The HCF of 546,458 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 546/715, 458/574?
Answer: GCF of Numerators as per given numbers 546/715, 458/574 is
GCF of Numerators i.e. for 546,458 is 2
LCM of denominators i.e. for 715,574 is 410410.
Thus, GCF of Fractions is 2/410410.Finally, GCF of Fractions for 546/715, 458/574 is 2/410410.