Use our free GCF of Fractions Calculator tool to compute the GCF of 69/96, 78/76, 23/36, 42/812 i.e 1/1110816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/96, 78/76, 23/36, 42/812.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/96,78/76,23/36,42/812
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 69/96,78/76,23/36,42/812, numerators are 69,78,23,42
Denominators are 96,76,36,812
The GCF of 69,78,23,42 is 1 .
LCM of 96,76,36,812 is 1110816.
The greatest common factor of 69/96,78/76,23/36,42/812 = [GCF of 69,78,23,42]/[LCM of 96,76,36,812]= 1/1110816
Therefore, the GCF of 69/96,78/76,23/36,42/812 is 1/1110816.
To find the highest common factor of 69,78,23,42, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 23 are 1, 23
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The HCF of 69,78,23,42 is 1.
Lets's calculate GCF of 69,78,23,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 23
:1,23
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 69,78,23,42 . The biggest common factor number is the GCF number.
So the greatest common factor 69,78,23,42 is 1.
Lets's calculate LCM of 96,76,36,812
2 | 96, 76, 36, 812 |
2 | 48, 38, 18, 406 |
3 | 24, 19, 9, 203 |
8, 19, 3, 203 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 8 x 19 x 3 x 203 = 1110816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1110816
Therefore, the GCF of Fractions 69/96,78/76,23/36,42/812 is 1/1110816
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 96,76,36,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,76,36,812) = 4
common factors(in case of two or more numbers have common factors) = 48
GCF(96,76,36,812) x common factors =4 x 48 = 192
LCM(96,76,36,812) = ( 96 × 76 × 36 × 812 ) / 192
LCM(96,76,36,812) = 213276672 / 192
LCM(96,76,36,812) = 1110816
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,78,23,42?
The HCF of 69,78,23,42 is 1
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 69/96, 78/76, 23/36, 42/812?
Answer: GCF of Numerators as per given numbers 69/96, 78/76, 23/36, 42/812 is
GCF of Numerators i.e. for 69,78,23,42 is 1
LCM of denominators i.e. for 96,76,36,812 is 1110816.
Thus, GCF of Fractions is 1/1110816.Finally, GCF of Fractions for 69/96, 78/76, 23/36, 42/812 is 1/1110816.