Use our free GCF of Fractions Calculator tool to compute the GCF of 4/41, 42/27, 40/142, 432/768 i.e 2/20120832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4/41, 42/27, 40/142, 432/768.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 4/41,42/27,40/142,432/768
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 4/41,42/27,40/142,432/768, numerators are 4,42,40,432
Denominators are 41,27,142,768
The GCF of 4,42,40,432 is 2 .
LCM of 41,27,142,768 is 20120832.
The greatest common factor of 4/41,42/27,40/142,432/768 = [GCF of 4,42,40,432]/[LCM of 41,27,142,768]= 2/20120832
Therefore, the GCF of 4/41,42/27,40/142,432/768 is 2/20120832.
To find the highest common factor of 4,42,40,432, we have to find the factors of both numbers and list the highest common factor.
The factors of 4 are 1, 2, 4
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
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 HCF of 4,42,40,432 is 2.
Lets's calculate GCF of 4,42,40,432
2 | 4, 42, 40, 432 |
2, 21, 20, 216 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 4
:1,2,4
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
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
Greatest Common Factor
We found the factors 4,42,40,432 . The biggest common factor number is the GCF number.
So the greatest common factor 4,42,40,432 is 2.
Lets's calculate LCM of 41,27,142,768
2 | 41, 27, 142, 768 |
3 | 41, 27, 71, 384 |
41, 9, 71, 128 |
∴ So the LCM of the given numbers is 2 x 3 x 41 x 9 x 71 x 128 = 20120832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20120832
Therefore, the GCF of Fractions 4/41,42/27,40/142,432/768 is 2/20120832
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 41,27,142,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(41,27,142,768) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(41,27,142,768) x common factors =1 x 6 = 6
LCM(41,27,142,768) = ( 41 × 27 × 142 × 768 ) / 6
LCM(41,27,142,768) = 120724992 / 6
LCM(41,27,142,768) = 20120832
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 4,42,40,432?
The HCF of 4,42,40,432 is 2
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 4/41, 42/27, 40/142, 432/768?
Answer: GCF of Numerators as per given numbers 4/41, 42/27, 40/142, 432/768 is
GCF of Numerators i.e. for 4,42,40,432 is 2
LCM of denominators i.e. for 41,27,142,768 is 20120832.
Thus, GCF of Fractions is 2/20120832.Finally, GCF of Fractions for 4/41, 42/27, 40/142, 432/768 is 2/20120832.