GCF of 5718/578, 2784/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5718/578, 2784/378 i.e 6/109242 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5718/578, 2784/378.
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 5718/578,2784/378?
Given fractions are 5718/578,2784/378
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 5718/578,2784/378, numerators are 5718,2784
Denominators are 578,378
The GCF of 5718,2784 is 6 .
LCM of 578,378 is 109242.
The greatest common factor of 5718/578,2784/378 = [GCF of 5718,2784]/[LCM of 578,378]= 6/109242
Therefore, the GCF of 5718/578,2784/378 is 6/109242.
To find the highest common factor of 5718,2784, we have to find the factors of both numbers and list the highest common factor.
The factors of 5718 are 1, 2, 3, 6, 953, 1906, 2859, 5718
The factors of 2784 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 32, 48, 58, 87, 96, 116, 174, 232, 348, 464, 696, 928, 1392, 2784
The HCF of 5718,2784 is 6.
Lets's calculate GCF of 5718,2784
| 2 | 5718, 2784 |
| 3 | 2859, 1392 |
| 953, 464 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 5718,2784 By Matching Biggest Common Factor Method
Now, list down the factors of 5718
:1,2,3,6,953,1906,2859,5718
Now, list down the factors of 2784
:1,2,3,4,6,8,12,16,24,29,32,48,58,87,96,116,174,232,348,464,696,928,1392,2784
Greatest Common Factor
We found the factors 5718,2784 . The biggest common factor number is the GCF number.
So the greatest common factor 5718,2784 is 6.
Lets's calculate LCM of 578,378
| 2 | 578, 378 |
| 289, 189 |
∴ So the LCM of the given numbers is 2 x 289 x 189 = 109242
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/109242
Therefore, the GCF of Fractions 5718/578,2784/378 is 6/109242
Least Common Multiple of 578,378 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 578,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,378) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,378) x common factors =2 x 1 = 2
LCM(578,378) = ( 578 × 378 ) / 2
LCM(578,378) = 218484 / 2
LCM(578,378) = 109242
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FAQs on GCF of Fractions of 5718/578, 2784/378
1. What is the HCF of 5718,2784?
The HCF of 5718,2784 is 6
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 5718/578, 2784/378?
Answer: GCF of Numerators as per given numbers 5718/578, 2784/378 is
GCF of Numerators i.e. for 5718,2784 is 6
LCM of denominators i.e. for 578,378 is 109242.
Thus, GCF of Fractions is 6/109242.Finally, GCF of Fractions for 5718/578, 2784/378 is 6/109242.