Use our free GCF of Fractions Calculator tool to compute the GCF of 423/468, 345/272 i.e 3/31824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 423/468, 345/272.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 423/468,345/272
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 423/468,345/272, numerators are 423,345
Denominators are 468,272
The GCF of 423,345 is 3 .
LCM of 468,272 is 31824.
The greatest common factor of 423/468,345/272 = [GCF of 423,345]/[LCM of 468,272]= 3/31824
Therefore, the GCF of 423/468,345/272 is 3/31824.
To find the highest common factor of 423,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 423 are 1, 3, 9, 47, 141, 423
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 423,345 is 3.
Lets's calculate GCF of 423,345
3 | 423, 345 |
141, 115 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 423
:1,3,9,47,141,423
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 423,345 . The biggest common factor number is the GCF number.
So the greatest common factor 423,345 is 3.
Lets's calculate LCM of 468,272
2 | 468, 272 |
2 | 234, 136 |
117, 68 |
∴ So the LCM of the given numbers is 2 x 2 x 117 x 68 = 31824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/31824
Therefore, the GCF of Fractions 423/468,345/272 is 3/31824
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 468,272 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(468,272) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(468,272) x common factors =4 x 1 = 4
LCM(468,272) = ( 468 × 272 ) / 4
LCM(468,272) = 127296 / 4
LCM(468,272) = 31824
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 423,345?
The HCF of 423,345 is 3
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 423/468, 345/272?
Answer: GCF of Numerators as per given numbers 423/468, 345/272 is
GCF of Numerators i.e. for 423,345 is 3
LCM of denominators i.e. for 468,272 is 31824.
Thus, GCF of Fractions is 3/31824.Finally, GCF of Fractions for 423/468, 345/272 is 3/31824.