GCF of 5328/286, 6864/299
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5328/286, 6864/299 i.e 48/6578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5328/286, 6864/299.
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 5328/286,6864/299?
Given fractions are 5328/286,6864/299
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 5328/286,6864/299, numerators are 5328,6864
Denominators are 286,299
The GCF of 5328,6864 is 48 .
LCM of 286,299 is 6578.
The greatest common factor of 5328/286,6864/299 = [GCF of 5328,6864]/[LCM of 286,299]= 48/6578
Therefore, the GCF of 5328/286,6864/299 is 48/6578.
To find the highest common factor of 5328,6864, we have to find the factors of both numbers and list the highest common factor.
The factors of 5328 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 37, 48, 72, 74, 111, 144, 148, 222, 296, 333, 444, 592, 666, 888, 1332, 1776, 2664, 5328
The factors of 6864 are 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432, 6864
The HCF of 5328,6864 is 48.
Lets's calculate GCF of 5328,6864
| 2 | 5328, 6864 |
| 2 | 2664, 3432 |
| 2 | 1332, 1716 |
| 2 | 666, 858 |
| 3 | 333, 429 |
| 111, 143 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Greatest Common Factor of 5328,6864 By Matching Biggest Common Factor Method
Now, list down the factors of 5328
:1,2,3,4,6,8,9,12,16,18,24,36,37,48,72,74,111,144,148,222,296,333,444,592,666,888,1332,1776,2664,5328
Now, list down the factors of 6864
:1,2,3,4,6,8,11,12,13,16,22,24,26,33,39,44,48,52,66,78,88,104,132,143,156,176,208,264,286,312,429,528,572,624,858,1144,1716,2288,3432,6864
Greatest Common Factor
We found the factors 5328,6864 . The biggest common factor number is the GCF number.
So the greatest common factor 5328,6864 is 48.
Lets's calculate LCM of 286,299
| 13 | 286, 299 |
| 22, 23 |
∴ So the LCM of the given numbers is 13 x 22 x 23 = 6578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/6578
Therefore, the GCF of Fractions 5328/286,6864/299 is 48/6578
Least Common Multiple of 286,299 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 286,299 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(286,299) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(286,299) x common factors =13 x 1 = 13
LCM(286,299) = ( 286 × 299 ) / 13
LCM(286,299) = 85514 / 13
LCM(286,299) = 6578
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FAQs on GCF of Fractions of 5328/286, 6864/299
1. What is the HCF of 5328,6864?
The HCF of 5328,6864 is 48
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 5328/286, 6864/299?
Answer: GCF of Numerators as per given numbers 5328/286, 6864/299 is
GCF of Numerators i.e. for 5328,6864 is 48
LCM of denominators i.e. for 286,299 is 6578.
Thus, GCF of Fractions is 48/6578.Finally, GCF of Fractions for 5328/286, 6864/299 is 48/6578.