Use our free GCF of Fractions Calculator tool to compute the GCF of 9/38, 42/92, 84/511, 129/287 i.e 3/36622348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9/38, 42/92, 84/511, 129/287.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/38,42/92,84/511,129/287
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 9/38,42/92,84/511,129/287, numerators are 9,42,84,129
Denominators are 38,92,511,287
The GCF of 9,42,84,129 is 3 .
LCM of 38,92,511,287 is 36622348.
The greatest common factor of 9/38,42/92,84/511,129/287 = [GCF of 9,42,84,129]/[LCM of 38,92,511,287]= 3/36622348
Therefore, the GCF of 9/38,42/92,84/511,129/287 is 3/36622348.
To find the highest common factor of 9,42,84,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 9 are 1, 3, 9
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 129 are 1, 3, 43, 129
The HCF of 9,42,84,129 is 3.
Lets's calculate GCF of 9,42,84,129
3 | 9, 42, 84, 129 |
3, 14, 28, 43 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 9,42,84,129 . The biggest common factor number is the GCF number.
So the greatest common factor 9,42,84,129 is 3.
Lets's calculate LCM of 38,92,511,287
2 | 38, 92, 511, 287 |
7 | 19, 46, 511, 287 |
19, 46, 73, 41 |
∴ So the LCM of the given numbers is 2 x 7 x 19 x 46 x 73 x 41 = 36622348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/36622348
Therefore, the GCF of Fractions 9/38,42/92,84/511,129/287 is 3/36622348
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 38,92,511,287 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,92,511,287) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(38,92,511,287) x common factors =1 x 14 = 14
LCM(38,92,511,287) = ( 38 × 92 × 511 × 287 ) / 14
LCM(38,92,511,287) = 512712872 / 14
LCM(38,92,511,287) = 36622348
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 9,42,84,129?
The HCF of 9,42,84,129 is 3
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 9/38, 42/92, 84/511, 129/287?
Answer: GCF of Numerators as per given numbers 9/38, 42/92, 84/511, 129/287 is
GCF of Numerators i.e. for 9,42,84,129 is 3
LCM of denominators i.e. for 38,92,511,287 is 36622348.
Thus, GCF of Fractions is 3/36622348.Finally, GCF of Fractions for 9/38, 42/92, 84/511, 129/287 is 3/36622348.