Use our free GCF of Fractions Calculator tool to compute the GCF of 172/954, 320/354 i.e 4/56286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/954, 320/354.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 172/954,320/354
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 172/954,320/354, numerators are 172,320
Denominators are 954,354
The GCF of 172,320 is 4 .
LCM of 954,354 is 56286.
The greatest common factor of 172/954,320/354 = [GCF of 172,320]/[LCM of 954,354]= 4/56286
Therefore, the GCF of 172/954,320/354 is 4/56286.
To find the highest common factor of 172,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 172 are 1, 2, 4, 43, 86, 172
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 172,320 is 4.
Lets's calculate GCF of 172,320
2 | 172, 320 |
2 | 86, 160 |
43, 80 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 172
:1,2,4,43,86,172
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 172,320 . The biggest common factor number is the GCF number.
So the greatest common factor 172,320 is 4.
Lets's calculate LCM of 954,354
2 | 954, 354 |
3 | 477, 177 |
159, 59 |
∴ So the LCM of the given numbers is 2 x 3 x 159 x 59 = 56286
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/56286
Therefore, the GCF of Fractions 172/954,320/354 is 4/56286
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 954,354 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(954,354) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(954,354) x common factors =6 x 1 = 6
LCM(954,354) = ( 954 × 354 ) / 6
LCM(954,354) = 337716 / 6
LCM(954,354) = 56286
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 172,320?
The HCF of 172,320 is 4
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 172/954, 320/354?
Answer: GCF of Numerators as per given numbers 172/954, 320/354 is
GCF of Numerators i.e. for 172,320 is 4
LCM of denominators i.e. for 954,354 is 56286.
Thus, GCF of Fractions is 4/56286.Finally, GCF of Fractions for 172/954, 320/354 is 4/56286.