GCF of 2134/254, 7584/5872
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2134/254, 7584/5872 i.e 2/745744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2134/254, 7584/5872.
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 2134/254,7584/5872?
Given fractions are 2134/254,7584/5872
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 2134/254,7584/5872, numerators are 2134,7584
Denominators are 254,5872
The GCF of 2134,7584 is 2 .
LCM of 254,5872 is 745744.
The greatest common factor of 2134/254,7584/5872 = [GCF of 2134,7584]/[LCM of 254,5872]= 2/745744
Therefore, the GCF of 2134/254,7584/5872 is 2/745744.
To find the highest common factor of 2134,7584, we have to find the factors of both numbers and list the highest common factor.
The factors of 2134 are 1, 2, 11, 22, 97, 194, 1067, 2134
The factors of 7584 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792, 7584
The HCF of 2134,7584 is 2.
Lets's calculate GCF of 2134,7584
| 2 | 2134, 7584 |
| 1067, 3792 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2134,7584 By Matching Biggest Common Factor Method
Now, list down the factors of 2134
:1,2,11,22,97,194,1067,2134
Now, list down the factors of 7584
:1,2,3,4,6,8,12,16,24,32,48,79,96,158,237,316,474,632,948,1264,1896,2528,3792,7584
Greatest Common Factor
We found the factors 2134,7584 . The biggest common factor number is the GCF number.
So the greatest common factor 2134,7584 is 2.
Lets's calculate LCM of 254,5872
| 2 | 254, 5872 |
| 127, 2936 |
∴ So the LCM of the given numbers is 2 x 127 x 2936 = 745744
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/745744
Therefore, the GCF of Fractions 2134/254,7584/5872 is 2/745744
Least Common Multiple of 254,5872 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 254,5872 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(254,5872) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(254,5872) x common factors =2 x 1 = 2
LCM(254,5872) = ( 254 × 5872 ) / 2
LCM(254,5872) = 1491488 / 2
LCM(254,5872) = 745744
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FAQs on GCF of Fractions of 2134/254, 7584/5872
1. What is the HCF of 2134,7584?
The HCF of 2134,7584 is 2
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 2134/254, 7584/5872?
Answer: GCF of Numerators as per given numbers 2134/254, 7584/5872 is
GCF of Numerators i.e. for 2134,7584 is 2
LCM of denominators i.e. for 254,5872 is 745744.
Thus, GCF of Fractions is 2/745744.Finally, GCF of Fractions for 2134/254, 7584/5872 is 2/745744.