GCF of 38/84, 57/12, 190/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/84, 57/12, 190/21 i.e 19/84 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/84, 57/12, 190/21.
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 38/84,57/12,190/21?
Given fractions are 38/84,57/12,190/21
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 38/84,57/12,190/21, numerators are 38,57,190
Denominators are 84,12,21
The GCF of 38,57,190 is 19 .
LCM of 84,12,21 is 84.
The greatest common factor of 38/84,57/12,190/21 = [GCF of 38,57,190]/[LCM of 84,12,21]= 19/84
Therefore, the GCF of 38/84,57/12,190/21 is 19/84.
To find the highest common factor of 38,57,190, 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 57 are 1, 3, 19, 57
The factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190
The HCF of 38,57,190 is 19.
Lets's calculate GCF of 38,57,190
| 19 | 38, 57, 190 |
| 2, 3, 10 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 38,57,190 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 57
:1,3,19,57
Now, list down the factors of 190
:1,2,5,10,19,38,95,190
Greatest Common Factor
We found the factors 38,57,190 . The biggest common factor number is the GCF number.
So the greatest common factor 38,57,190 is 19.
Lets's calculate LCM of 84,12,21
| 2 | 84, 12, 21 |
| 2 | 42, 6, 21 |
| 3 | 21, 3, 21 |
| 7 | 7, 1, 7 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 1 x 1 = 84
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/84
Therefore, the GCF of Fractions 38/84,57/12,190/21 is 19/84
Least Common Multiple of 84,12,21 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 84,12,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,12,21) = 3
common factors(in case of two or more numbers have common factors) = 84
GCF(84,12,21) x common factors =3 x 84 = 252
LCM(84,12,21) = ( 84 × 12 × 21 ) / 252
LCM(84,12,21) = 21168 / 252
LCM(84,12,21) = 84
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FAQs on GCF of Fractions of 38/84, 57/12, 190/21
1. What is the HCF of 38,57,190?
The HCF of 38,57,190 is 19
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 38/84, 57/12, 190/21?
Answer: GCF of Numerators as per given numbers 38/84, 57/12, 190/21 is
GCF of Numerators i.e. for 38,57,190 is 19
LCM of denominators i.e. for 84,12,21 is 84.
Thus, GCF of Fractions is 19/84.Finally, GCF of Fractions for 38/84, 57/12, 190/21 is 19/84.