GCF of 278/278, 257/542
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 278/278, 257/542 i.e 1/75338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/278, 257/542.
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 278/278,257/542?
Given fractions are 278/278,257/542
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 278/278,257/542, numerators are 278,257
Denominators are 278,542
The GCF of 278,257 is 1 .
LCM of 278,542 is 75338.
The greatest common factor of 278/278,257/542 = [GCF of 278,257]/[LCM of 278,542]= 1/75338
Therefore, the GCF of 278/278,257/542 is 1/75338.
To find the highest common factor of 278,257, 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 257 are 1, 257
The HCF of 278,257 is 1.
Lets's calculate GCF of 278,257
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 278,257 By Matching Biggest Common Factor Method
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 257
:1,257
Greatest Common Factor
We found the factors 278,257 . The biggest common factor number is the GCF number.
So the greatest common factor 278,257 is 1.
Lets's calculate LCM of 278,542
| 2 | 278, 542 |
| 139, 271 |
∴ So the LCM of the given numbers is 2 x 139 x 271 = 75338
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75338
Therefore, the GCF of Fractions 278/278,257/542 is 1/75338
Least Common Multiple of 278,542 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 278,542 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,542) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,542) x common factors =2 x 1 = 2
LCM(278,542) = ( 278 × 542 ) / 2
LCM(278,542) = 150676 / 2
LCM(278,542) = 75338
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FAQs on GCF of Fractions of 278/278, 257/542
1. What is the HCF of 278,257?
The HCF of 278,257 is 1
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 278/278, 257/542?
Answer: GCF of Numerators as per given numbers 278/278, 257/542 is
GCF of Numerators i.e. for 278,257 is 1
LCM of denominators i.e. for 278,542 is 75338.
Thus, GCF of Fractions is 1/75338.Finally, GCF of Fractions for 278/278, 257/542 is 1/75338.