GCF of 2856/343, 2784/304
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2856/343, 2784/304 i.e 24/104272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2856/343, 2784/304.
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 2856/343,2784/304?
Given fractions are 2856/343,2784/304
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 2856/343,2784/304, numerators are 2856,2784
Denominators are 343,304
The GCF of 2856,2784 is 24 .
LCM of 343,304 is 104272.
The greatest common factor of 2856/343,2784/304 = [GCF of 2856,2784]/[LCM of 343,304]= 24/104272
Therefore, the GCF of 2856/343,2784/304 is 24/104272.
To find the highest common factor of 2856,2784, we have to find the factors of both numbers and list the highest common factor.
The factors of 2856 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952, 1428, 2856
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 2856,2784 is 24.
Lets's calculate GCF of 2856,2784
| 2 | 2856, 2784 |
| 2 | 1428, 1392 |
| 2 | 714, 696 |
| 3 | 357, 348 |
| 119, 116 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 2856,2784 By Matching Biggest Common Factor Method
Now, list down the factors of 2856
:1,2,3,4,6,7,8,12,14,17,21,24,28,34,42,51,56,68,84,102,119,136,168,204,238,357,408,476,714,952,1428,2856
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 2856,2784 . The biggest common factor number is the GCF number.
So the greatest common factor 2856,2784 is 24.
Lets's calculate LCM of 343,304
Given numbers has no common factors except 1. So, there LCM is their product i.e 104272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/104272
Therefore, the GCF of Fractions 2856/343,2784/304 is 24/104272
Least Common Multiple of 343,304 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 343,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,304) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(343,304) x common factors =1 x 1 = 1
LCM(343,304) = ( 343 × 304 ) / 1
LCM(343,304) = 104272 / 1
LCM(343,304) = 104272
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FAQs on GCF of Fractions of 2856/343, 2784/304
1. What is the HCF of 2856,2784?
The HCF of 2856,2784 is 24
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 2856/343, 2784/304?
Answer: GCF of Numerators as per given numbers 2856/343, 2784/304 is
GCF of Numerators i.e. for 2856,2784 is 24
LCM of denominators i.e. for 343,304 is 104272.
Thus, GCF of Fractions is 24/104272.Finally, GCF of Fractions for 2856/343, 2784/304 is 24/104272.