Use our free GCF of Fractions Calculator tool to compute the GCF of 144/411, 117/823 i.e 9/338253 easily. The following is the detailed procedure to determine the greatest common factor of fractions 144/411, 117/823.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 144/411,117/823
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 144/411,117/823, numerators are 144,117
Denominators are 411,823
The GCF of 144,117 is 9 .
LCM of 411,823 is 338253.
The greatest common factor of 144/411,117/823 = [GCF of 144,117]/[LCM of 411,823]= 9/338253
Therefore, the GCF of 144/411,117/823 is 9/338253.
To find the highest common factor of 144,117, we have to find the factors of both numbers and list the highest common factor.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 117 are 1, 3, 9, 13, 39, 117
The HCF of 144,117 is 9.
Lets's calculate GCF of 144,117
3 | 144, 117 |
3 | 48, 39 |
16, 13 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 144,117 . The biggest common factor number is the GCF number.
So the greatest common factor 144,117 is 9.
Lets's calculate LCM of 411,823
Given numbers has no common factors except 1. So, there LCM is their product i.e 338253
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/338253
Therefore, the GCF of Fractions 144/411,117/823 is 9/338253
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 411,823 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(411,823) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(411,823) x common factors =1 x 1 = 1
LCM(411,823) = ( 411 × 823 ) / 1
LCM(411,823) = 338253 / 1
LCM(411,823) = 338253
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 144,117?
The HCF of 144,117 is 9
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 144/411, 117/823?
Answer: GCF of Numerators as per given numbers 144/411, 117/823 is
GCF of Numerators i.e. for 144,117 is 9
LCM of denominators i.e. for 411,823 is 338253.
Thus, GCF of Fractions is 9/338253.Finally, GCF of Fractions for 144/411, 117/823 is 9/338253.