GCF of 2138/420, 5300/588
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2138/420, 5300/588 i.e 2/2940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2138/420, 5300/588.
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 2138/420,5300/588?
Given fractions are 2138/420,5300/588
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 2138/420,5300/588, numerators are 2138,5300
Denominators are 420,588
The GCF of 2138,5300 is 2 .
LCM of 420,588 is 2940.
The greatest common factor of 2138/420,5300/588 = [GCF of 2138,5300]/[LCM of 420,588]= 2/2940
Therefore, the GCF of 2138/420,5300/588 is 2/2940.
To find the highest common factor of 2138,5300, we have to find the factors of both numbers and list the highest common factor.
The factors of 2138 are 1, 2, 1069, 2138
The factors of 5300 are 1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650, 5300
The HCF of 2138,5300 is 2.
Lets's calculate GCF of 2138,5300
| 2 | 2138, 5300 |
| 1069, 2650 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2138,5300 By Matching Biggest Common Factor Method
Now, list down the factors of 2138
:1,2,1069,2138
Now, list down the factors of 5300
:1,2,4,5,10,20,25,50,53,100,106,212,265,530,1060,1325,2650,5300
Greatest Common Factor
We found the factors 2138,5300 . The biggest common factor number is the GCF number.
So the greatest common factor 2138,5300 is 2.
Lets's calculate LCM of 420,588
| 2 | 420, 588 |
| 2 | 210, 294 |
| 3 | 105, 147 |
| 7 | 35, 49 |
| 5, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 5 x 7 = 2940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2940
Therefore, the GCF of Fractions 2138/420,5300/588 is 2/2940
Least Common Multiple of 420,588 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 420,588 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,588) = 84
common factors(in case of two or more numbers have common factors) = 1
GCF(420,588) x common factors =84 x 1 = 84
LCM(420,588) = ( 420 × 588 ) / 84
LCM(420,588) = 246960 / 84
LCM(420,588) = 2940
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FAQs on GCF of Fractions of 2138/420, 5300/588
1. What is the HCF of 2138,5300?
The HCF of 2138,5300 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 2138/420, 5300/588?
Answer: GCF of Numerators as per given numbers 2138/420, 5300/588 is
GCF of Numerators i.e. for 2138,5300 is 2
LCM of denominators i.e. for 420,588 is 2940.
Thus, GCF of Fractions is 2/2940.Finally, GCF of Fractions for 2138/420, 5300/588 is 2/2940.