GCF of 2571/278, 7668/2678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2571/278, 7668/2678 i.e 3/372242 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2571/278, 7668/2678.
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 2571/278,7668/2678?
Given fractions are 2571/278,7668/2678
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 2571/278,7668/2678, numerators are 2571,7668
Denominators are 278,2678
The GCF of 2571,7668 is 3 .
LCM of 278,2678 is 372242.
The greatest common factor of 2571/278,7668/2678 = [GCF of 2571,7668]/[LCM of 278,2678]= 3/372242
Therefore, the GCF of 2571/278,7668/2678 is 3/372242.
To find the highest common factor of 2571,7668, we have to find the factors of both numbers and list the highest common factor.
The factors of 2571 are 1, 3, 857, 2571
The factors of 7668 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 71, 108, 142, 213, 284, 426, 639, 852, 1278, 1917, 2556, 3834, 7668
The HCF of 2571,7668 is 3.
Lets's calculate GCF of 2571,7668
| 3 | 2571, 7668 |
| 857, 2556 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2571,7668 By Matching Biggest Common Factor Method
Now, list down the factors of 2571
:1,3,857,2571
Now, list down the factors of 7668
:1,2,3,4,6,9,12,18,27,36,54,71,108,142,213,284,426,639,852,1278,1917,2556,3834,7668
Greatest Common Factor
We found the factors 2571,7668 . The biggest common factor number is the GCF number.
So the greatest common factor 2571,7668 is 3.
Lets's calculate LCM of 278,2678
| 2 | 278, 2678 |
| 139, 1339 |
∴ So the LCM of the given numbers is 2 x 139 x 1339 = 372242
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/372242
Therefore, the GCF of Fractions 2571/278,7668/2678 is 3/372242
Least Common Multiple of 278,2678 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 278,2678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,2678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,2678) x common factors =2 x 1 = 2
LCM(278,2678) = ( 278 × 2678 ) / 2
LCM(278,2678) = 744484 / 2
LCM(278,2678) = 372242
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FAQs on GCF of Fractions of 2571/278, 7668/2678
1. What is the HCF of 2571,7668?
The HCF of 2571,7668 is 3
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 2571/278, 7668/2678?
Answer: GCF of Numerators as per given numbers 2571/278, 7668/2678 is
GCF of Numerators i.e. for 2571,7668 is 3
LCM of denominators i.e. for 278,2678 is 372242.
Thus, GCF of Fractions is 3/372242.Finally, GCF of Fractions for 2571/278, 7668/2678 is 3/372242.