GCF of 38/12, 322/68, 415/922
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/12, 322/68, 415/922 i.e 1/94044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/12, 322/68, 415/922.
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 38/12,322/68,415/922?
Given fractions are 38/12,322/68,415/922
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 38/12,322/68,415/922, numerators are 38,322,415
Denominators are 12,68,922
The GCF of 38,322,415 is 1 .
LCM of 12,68,922 is 94044.
The greatest common factor of 38/12,322/68,415/922 = [GCF of 38,322,415]/[LCM of 12,68,922]= 1/94044
Therefore, the GCF of 38/12,322/68,415/922 is 1/94044.
To find the highest common factor of 38,322,415, 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 322 are 1, 2, 7, 14, 23, 46, 161, 322
The factors of 415 are 1, 5, 83, 415
The HCF of 38,322,415 is 1.
Lets's calculate GCF of 38,322,415
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 38,322,415 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Now, list down the factors of 415
:1,5,83,415
Greatest Common Factor
We found the factors 38,322,415 . The biggest common factor number is the GCF number.
So the greatest common factor 38,322,415 is 1.
Lets's calculate LCM of 12,68,922
| 2 | 12, 68, 922 |
| 2 | 6, 34, 461 |
| 3, 17, 461 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 461 = 94044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/94044
Therefore, the GCF of Fractions 38/12,322/68,415/922 is 1/94044
Least Common Multiple of 12,68,922 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 12,68,922 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,68,922) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(12,68,922) x common factors =2 x 4 = 8
LCM(12,68,922) = ( 12 × 68 × 922 ) / 8
LCM(12,68,922) = 752352 / 8
LCM(12,68,922) = 94044
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 38/12, 322/68, 415/922
1. What is the HCF of 38,322,415?
The HCF of 38,322,415 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 38/12, 322/68, 415/922?
Answer: GCF of Numerators as per given numbers 38/12, 322/68, 415/922 is
GCF of Numerators i.e. for 38,322,415 is 1
LCM of denominators i.e. for 12,68,922 is 94044.
Thus, GCF of Fractions is 1/94044.Finally, GCF of Fractions for 38/12, 322/68, 415/922 is 1/94044.