Use our free GCF of Fractions Calculator tool to compute the GCF of 971/172, 390/408 i.e 1/17544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 971/172, 390/408.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 971/172,390/408
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 971/172,390/408, numerators are 971,390
Denominators are 172,408
The GCF of 971,390 is 1 .
LCM of 172,408 is 17544.
The greatest common factor of 971/172,390/408 = [GCF of 971,390]/[LCM of 172,408]= 1/17544
Therefore, the GCF of 971/172,390/408 is 1/17544.
To find the highest common factor of 971,390, we have to find the factors of both numbers and list the highest common factor.
The factors of 971 are 1, 971
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The HCF of 971,390 is 1.
Lets's calculate GCF of 971,390
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 971
:1,971
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Greatest Common Factor
We found the factors 971,390 . The biggest common factor number is the GCF number.
So the greatest common factor 971,390 is 1.
Lets's calculate LCM of 172,408
2 | 172, 408 |
2 | 86, 204 |
43, 102 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 102 = 17544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17544
Therefore, the GCF of Fractions 971/172,390/408 is 1/17544
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 172,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,408) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(172,408) x common factors =4 x 1 = 4
LCM(172,408) = ( 172 × 408 ) / 4
LCM(172,408) = 70176 / 4
LCM(172,408) = 17544
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 971,390?
The HCF of 971,390 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 971/172, 390/408?
Answer: GCF of Numerators as per given numbers 971/172, 390/408 is
GCF of Numerators i.e. for 971,390 is 1
LCM of denominators i.e. for 172,408 is 17544.
Thus, GCF of Fractions is 1/17544.Finally, GCF of Fractions for 971/172, 390/408 is 1/17544.