GCF of 194/524, 4138/1986
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 194/524, 4138/1986 i.e 2/520332 easily. The following is the detailed procedure to determine the greatest common factor of fractions 194/524, 4138/1986.
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 194/524,4138/1986?
Given fractions are 194/524,4138/1986
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 194/524,4138/1986, numerators are 194,4138
Denominators are 524,1986
The GCF of 194,4138 is 2 .
LCM of 524,1986 is 520332.
The greatest common factor of 194/524,4138/1986 = [GCF of 194,4138]/[LCM of 524,1986]= 2/520332
Therefore, the GCF of 194/524,4138/1986 is 2/520332.
To find the highest common factor of 194,4138, we have to find the factors of both numbers and list the highest common factor.
The factors of 194 are 1, 2, 97, 194
The factors of 4138 are 1, 2, 2069, 4138
The HCF of 194,4138 is 2.
Lets's calculate GCF of 194,4138
| 2 | 194, 4138 |
| 97, 2069 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 194,4138 By Matching Biggest Common Factor Method
Now, list down the factors of 194
:1,2,97,194
Now, list down the factors of 4138
:1,2,2069,4138
Greatest Common Factor
We found the factors 194,4138 . The biggest common factor number is the GCF number.
So the greatest common factor 194,4138 is 2.
Lets's calculate LCM of 524,1986
| 2 | 524, 1986 |
| 262, 993 |
∴ So the LCM of the given numbers is 2 x 262 x 993 = 520332
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/520332
Therefore, the GCF of Fractions 194/524,4138/1986 is 2/520332
Least Common Multiple of 524,1986 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 524,1986 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(524,1986) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(524,1986) x common factors =2 x 1 = 2
LCM(524,1986) = ( 524 × 1986 ) / 2
LCM(524,1986) = 1040664 / 2
LCM(524,1986) = 520332
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FAQs on GCF of Fractions of 194/524, 4138/1986
1. What is the HCF of 194,4138?
The HCF of 194,4138 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 194/524, 4138/1986?
Answer: GCF of Numerators as per given numbers 194/524, 4138/1986 is
GCF of Numerators i.e. for 194,4138 is 2
LCM of denominators i.e. for 524,1986 is 520332.
Thus, GCF of Fractions is 2/520332.Finally, GCF of Fractions for 194/524, 4138/1986 is 2/520332.