Use our free GCF of Fractions Calculator tool to compute the GCF of 17/32, 320/59, 421/448 i.e 1/26432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/32, 320/59, 421/448.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/32,320/59,421/448
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 17/32,320/59,421/448, numerators are 17,320,421
Denominators are 32,59,448
The GCF of 17,320,421 is 1 .
LCM of 32,59,448 is 26432.
The greatest common factor of 17/32,320/59,421/448 = [GCF of 17,320,421]/[LCM of 32,59,448]= 1/26432
Therefore, the GCF of 17/32,320/59,421/448 is 1/26432.
To find the highest common factor of 17,320,421, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The factors of 421 are 1, 421
The HCF of 17,320,421 is 1.
Lets's calculate GCF of 17,320,421
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 17
:1,17
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Now, list down the factors of 421
:1,421
Greatest Common Factor
We found the factors 17,320,421 . The biggest common factor number is the GCF number.
So the greatest common factor 17,320,421 is 1.
Lets's calculate LCM of 32,59,448
2 | 32, 59, 448 |
2 | 16, 59, 224 |
2 | 8, 59, 112 |
2 | 4, 59, 56 |
2 | 2, 59, 28 |
1, 59, 14 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 59 x 14 = 26432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26432
Therefore, the GCF of Fractions 17/32,320/59,421/448 is 1/26432
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 32,59,448 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,59,448) = 1
common factors(in case of two or more numbers have common factors) = 32
GCF(32,59,448) x common factors =1 x 32 = 32
LCM(32,59,448) = ( 32 × 59 × 448 ) / 32
LCM(32,59,448) = 845824 / 32
LCM(32,59,448) = 26432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,320,421?
The HCF of 17,320,421 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 17/32, 320/59, 421/448?
Answer: GCF of Numerators as per given numbers 17/32, 320/59, 421/448 is
GCF of Numerators i.e. for 17,320,421 is 1
LCM of denominators i.e. for 32,59,448 is 26432.
Thus, GCF of Fractions is 1/26432.Finally, GCF of Fractions for 17/32, 320/59, 421/448 is 1/26432.