GCF of 38/123, 54/133, 321/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/123, 54/133, 321/978 i.e 1/5333034 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/123, 54/133, 321/978.
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 38/123,54/133,321/978?
Given fractions are 38/123,54/133,321/978
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 38/123,54/133,321/978, numerators are 38,54,321
Denominators are 123,133,978
The GCF of 38,54,321 is 1 .
LCM of 123,133,978 is 5333034.
The greatest common factor of 38/123,54/133,321/978 = [GCF of 38,54,321]/[LCM of 123,133,978]= 1/5333034
Therefore, the GCF of 38/123,54/133,321/978 is 1/5333034.
To find the highest common factor of 38,54,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 38 are 1, 2, 19, 38
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 321 are 1, 3, 107, 321
The HCF of 38,54,321 is 1.
Lets's calculate GCF of 38,54,321
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 38,54,321 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 38,54,321 . The biggest common factor number is the GCF number.
So the greatest common factor 38,54,321 is 1.
Lets's calculate LCM of 123,133,978
| 3 | 123, 133, 978 |
| 41, 133, 326 |
∴ So the LCM of the given numbers is 3 x 41 x 133 x 326 = 5333034
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5333034
Therefore, the GCF of Fractions 38/123,54/133,321/978 is 1/5333034
Least Common Multiple of 123,133,978 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 123,133,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,133,978) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(123,133,978) x common factors =1 x 3 = 3
LCM(123,133,978) = ( 123 × 133 × 978 ) / 3
LCM(123,133,978) = 15999102 / 3
LCM(123,133,978) = 5333034
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FAQs on GCF of Fractions of 38/123, 54/133, 321/978
1. What is the HCF of 38,54,321?
The HCF of 38,54,321 is 1
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 38/123, 54/133, 321/978?
Answer: GCF of Numerators as per given numbers 38/123, 54/133, 321/978 is
GCF of Numerators i.e. for 38,54,321 is 1
LCM of denominators i.e. for 123,133,978 is 5333034.
Thus, GCF of Fractions is 1/5333034.Finally, GCF of Fractions for 38/123, 54/133, 321/978 is 1/5333034.