GCF of 278/65, 538/403
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 278/65, 538/403 i.e 2/2015 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/65, 538/403.
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 278/65,538/403?
Given fractions are 278/65,538/403
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 278/65,538/403, numerators are 278,538
Denominators are 65,403
The GCF of 278,538 is 2 .
LCM of 65,403 is 2015.
The greatest common factor of 278/65,538/403 = [GCF of 278,538]/[LCM of 65,403]= 2/2015
Therefore, the GCF of 278/65,538/403 is 2/2015.
To find the highest common factor of 278,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 538 are 1, 2, 269, 538
The HCF of 278,538 is 2.
Lets's calculate GCF of 278,538
| 2 | 278, 538 |
| 139, 269 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 278,538 By Matching Biggest Common Factor Method
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 278,538 . The biggest common factor number is the GCF number.
So the greatest common factor 278,538 is 2.
Lets's calculate LCM of 65,403
| 13 | 65, 403 |
| 5, 31 |
∴ So the LCM of the given numbers is 13 x 5 x 31 = 2015
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2015
Therefore, the GCF of Fractions 278/65,538/403 is 2/2015
Least Common Multiple of 65,403 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 65,403 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,403) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(65,403) x common factors =13 x 1 = 13
LCM(65,403) = ( 65 × 403 ) / 13
LCM(65,403) = 26195 / 13
LCM(65,403) = 2015
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FAQs on GCF of Fractions of 278/65, 538/403
1. What is the HCF of 278,538?
The HCF of 278,538 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 278/65, 538/403?
Answer: GCF of Numerators as per given numbers 278/65, 538/403 is
GCF of Numerators i.e. for 278,538 is 2
LCM of denominators i.e. for 65,403 is 2015.
Thus, GCF of Fractions is 2/2015.Finally, GCF of Fractions for 278/65, 538/403 is 2/2015.