GCF of 575/278, 310/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 575/278, 310/728 i.e 5/101192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 575/278, 310/728.
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 575/278,310/728?
Given fractions are 575/278,310/728
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 575/278,310/728, numerators are 575,310
Denominators are 278,728
The GCF of 575,310 is 5 .
LCM of 278,728 is 101192.
The greatest common factor of 575/278,310/728 = [GCF of 575,310]/[LCM of 278,728]= 5/101192
Therefore, the GCF of 575/278,310/728 is 5/101192.
To find the highest common factor of 575,310, we have to find the factors of both numbers and list the highest common factor.
The factors of 575 are 1, 5, 23, 25, 115, 575
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 575,310 is 5.
Lets's calculate GCF of 575,310
| 5 | 575, 310 |
| 115, 62 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 575,310 By Matching Biggest Common Factor Method
Now, list down the factors of 575
:1,5,23,25,115,575
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 575,310 . The biggest common factor number is the GCF number.
So the greatest common factor 575,310 is 5.
Lets's calculate LCM of 278,728
| 2 | 278, 728 |
| 139, 364 |
∴ So the LCM of the given numbers is 2 x 139 x 364 = 101192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/101192
Therefore, the GCF of Fractions 575/278,310/728 is 5/101192
Least Common Multiple of 278,728 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 278,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,728) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,728) x common factors =2 x 1 = 2
LCM(278,728) = ( 278 × 728 ) / 2
LCM(278,728) = 202384 / 2
LCM(278,728) = 101192
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FAQs on GCF of Fractions of 575/278, 310/728
1. What is the HCF of 575,310?
The HCF of 575,310 is 5
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 575/278, 310/728?
Answer: GCF of Numerators as per given numbers 575/278, 310/728 is
GCF of Numerators i.e. for 575,310 is 5
LCM of denominators i.e. for 278,728 is 101192.
Thus, GCF of Fractions is 5/101192.Finally, GCF of Fractions for 575/278, 310/728 is 5/101192.