GCF of 538/40, 238/5200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 538/40, 238/5200 i.e 2/5200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 538/40, 238/5200.
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 538/40,238/5200?
Given fractions are 538/40,238/5200
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 538/40,238/5200, numerators are 538,238
Denominators are 40,5200
The GCF of 538,238 is 2 .
LCM of 40,5200 is 5200.
The greatest common factor of 538/40,238/5200 = [GCF of 538,238]/[LCM of 40,5200]= 2/5200
Therefore, the GCF of 538/40,238/5200 is 2/5200.
To find the highest common factor of 538,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 538 are 1, 2, 269, 538
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 538,238 is 2.
Lets's calculate GCF of 538,238
| 2 | 538, 238 |
| 269, 119 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 538,238 By Matching Biggest Common Factor Method
Now, list down the factors of 538
:1,2,269,538
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 538,238 . The biggest common factor number is the GCF number.
So the greatest common factor 538,238 is 2.
Lets's calculate LCM of 40,5200
| 2 | 40, 5200 |
| 2 | 20, 2600 |
| 2 | 10, 1300 |
| 5 | 5, 650 |
| 1, 130 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 130 = 5200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5200
Therefore, the GCF of Fractions 538/40,238/5200 is 2/5200
Least Common Multiple of 40,5200 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 40,5200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,5200) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(40,5200) x common factors =40 x 1 = 40
LCM(40,5200) = ( 40 × 5200 ) / 40
LCM(40,5200) = 208000 / 40
LCM(40,5200) = 5200
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FAQs on GCF of Fractions of 538/40, 238/5200
1. What is the HCF of 538,238?
The HCF of 538,238 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 538/40, 238/5200?
Answer: GCF of Numerators as per given numbers 538/40, 238/5200 is
GCF of Numerators i.e. for 538,238 is 2
LCM of denominators i.e. for 40,5200 is 5200.
Thus, GCF of Fractions is 2/5200.Finally, GCF of Fractions for 538/40, 238/5200 is 2/5200.