Use our free GCF of Fractions Calculator tool to compute the GCF of 648/192, 429/520 i.e 3/12480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 648/192, 429/520.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 648/192,429/520
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 648/192,429/520, numerators are 648,429
Denominators are 192,520
The GCF of 648,429 is 3 .
LCM of 192,520 is 12480.
The greatest common factor of 648/192,429/520 = [GCF of 648,429]/[LCM of 192,520]= 3/12480
Therefore, the GCF of 648/192,429/520 is 3/12480.
To find the highest common factor of 648,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 648,429 is 3.
Lets's calculate GCF of 648,429
3 | 648, 429 |
216, 143 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 648,429 . The biggest common factor number is the GCF number.
So the greatest common factor 648,429 is 3.
Lets's calculate LCM of 192,520
2 | 192, 520 |
2 | 96, 260 |
2 | 48, 130 |
24, 65 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 24 x 65 = 12480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/12480
Therefore, the GCF of Fractions 648/192,429/520 is 3/12480
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 192,520 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,520) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(192,520) x common factors =8 x 1 = 8
LCM(192,520) = ( 192 × 520 ) / 8
LCM(192,520) = 99840 / 8
LCM(192,520) = 12480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 648,429?
The HCF of 648,429 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 648/192, 429/520?
Answer: GCF of Numerators as per given numbers 648/192, 429/520 is
GCF of Numerators i.e. for 648,429 is 3
LCM of denominators i.e. for 192,520 is 12480.
Thus, GCF of Fractions is 3/12480.Finally, GCF of Fractions for 648/192, 429/520 is 3/12480.