Use our free GCF of Fractions Calculator tool to compute the GCF of 432/454, 342/538 i.e 18/122126 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/454, 342/538.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 432/454,342/538
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 432/454,342/538, numerators are 432,342
Denominators are 454,538
The GCF of 432,342 is 18 .
LCM of 454,538 is 122126.
The greatest common factor of 432/454,342/538 = [GCF of 432,342]/[LCM of 454,538]= 18/122126
Therefore, the GCF of 432/454,342/538 is 18/122126.
To find the highest common factor of 432,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 432,342 is 18.
Lets's calculate GCF of 432,342
2 | 432, 342 |
3 | 216, 171 |
3 | 72, 57 |
24, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 432,342 . The biggest common factor number is the GCF number.
So the greatest common factor 432,342 is 18.
Lets's calculate LCM of 454,538
2 | 454, 538 |
227, 269 |
∴ So the LCM of the given numbers is 2 x 227 x 269 = 122126
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/122126
Therefore, the GCF of Fractions 432/454,342/538 is 18/122126
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 454,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,538) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,538) x common factors =2 x 1 = 2
LCM(454,538) = ( 454 × 538 ) / 2
LCM(454,538) = 244252 / 2
LCM(454,538) = 122126
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 432,342?
The HCF of 432,342 is 18
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 432/454, 342/538?
Answer: GCF of Numerators as per given numbers 432/454, 342/538 is
GCF of Numerators i.e. for 432,342 is 18
LCM of denominators i.e. for 454,538 is 122126.
Thus, GCF of Fractions is 18/122126.Finally, GCF of Fractions for 432/454, 342/538 is 18/122126.