Use our free GCF of Fractions Calculator tool to compute the GCF of 1/38, 71/38, 27/564, 252/390 i.e 1/696540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/38, 71/38, 27/564, 252/390.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1/38,71/38,27/564,252/390
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 1/38,71/38,27/564,252/390, numerators are 1,71,27,252
Denominators are 38,38,564,390
The GCF of 1,71,27,252 is 1 .
LCM of 38,38,564,390 is 696540.
The greatest common factor of 1/38,71/38,27/564,252/390 = [GCF of 1,71,27,252]/[LCM of 38,38,564,390]= 1/696540
Therefore, the GCF of 1/38,71/38,27/564,252/390 is 1/696540.
To find the highest common factor of 1,71,27,252, we have to find the factors of both numbers and list the highest common factor.
The factors of 1 are 1
The factors of 71 are 1, 71
The factors of 27 are 1, 3, 9, 27
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The HCF of 1,71,27,252 is 1.
Lets's calculate GCF of 1,71,27,252
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 1
:1
Now, list down the factors of 71
:1,71
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Greatest Common Factor
We found the factors 1,71,27,252 . The biggest common factor number is the GCF number.
So the greatest common factor 1,71,27,252 is 1.
Lets's calculate LCM of 38,38,564,390
2 | 38, 38, 564, 390 |
3 | 19, 19, 282, 195 |
19 | 19, 19, 94, 65 |
1, 1, 94, 65 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 1 x 1 x 94 x 65 = 696540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/696540
Therefore, the GCF of Fractions 1/38,71/38,27/564,252/390 is 1/696540
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 38,38,564,390 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,38,564,390) = 2
common factors(in case of two or more numbers have common factors) = 228
GCF(38,38,564,390) x common factors =2 x 228 = 456
LCM(38,38,564,390) = ( 38 × 38 × 564 × 390 ) / 456
LCM(38,38,564,390) = 317622240 / 456
LCM(38,38,564,390) = 696540
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1,71,27,252?
The HCF of 1,71,27,252 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 1/38, 71/38, 27/564, 252/390?
Answer: GCF of Numerators as per given numbers 1/38, 71/38, 27/564, 252/390 is
GCF of Numerators i.e. for 1,71,27,252 is 1
LCM of denominators i.e. for 38,38,564,390 is 696540.
Thus, GCF of Fractions is 1/696540.Finally, GCF of Fractions for 1/38, 71/38, 27/564, 252/390 is 1/696540.