Use our free GCF of Fractions Calculator tool to compute the GCF of 38/75, 858/69, 432/425 i.e 2/29325 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/75, 858/69, 432/425.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 38/75,858/69,432/425
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 38/75,858/69,432/425, numerators are 38,858,432
Denominators are 75,69,425
The GCF of 38,858,432 is 2 .
LCM of 75,69,425 is 29325.
The greatest common factor of 38/75,858/69,432/425 = [GCF of 38,858,432]/[LCM of 75,69,425]= 2/29325
Therefore, the GCF of 38/75,858/69,432/425 is 2/29325.
To find the highest common factor of 38,858,432, 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 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The HCF of 38,858,432 is 2.
Lets's calculate GCF of 38,858,432
2 | 38, 858, 432 |
19, 429, 216 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Greatest Common Factor
We found the factors 38,858,432 . The biggest common factor number is the GCF number.
So the greatest common factor 38,858,432 is 2.
Lets's calculate LCM of 75,69,425
3 | 75, 69, 425 |
5 | 25, 23, 425 |
5 | 5, 23, 85 |
1, 23, 17 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 1 x 23 x 17 = 29325
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29325
Therefore, the GCF of Fractions 38/75,858/69,432/425 is 2/29325
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 75,69,425 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,69,425) = 1
common factors(in case of two or more numbers have common factors) = 75
GCF(75,69,425) x common factors =1 x 75 = 75
LCM(75,69,425) = ( 75 × 69 × 425 ) / 75
LCM(75,69,425) = 2199375 / 75
LCM(75,69,425) = 29325
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 38,858,432?
The HCF of 38,858,432 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 38/75, 858/69, 432/425?
Answer: GCF of Numerators as per given numbers 38/75, 858/69, 432/425 is
GCF of Numerators i.e. for 38,858,432 is 2
LCM of denominators i.e. for 75,69,425 is 29325.
Thus, GCF of Fractions is 2/29325.Finally, GCF of Fractions for 38/75, 858/69, 432/425 is 2/29325.