Use our free GCF of Fractions Calculator tool to compute the GCF of 74/84, 156/27, 222/104 i.e 2/19656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/84, 156/27, 222/104.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 74/84,156/27,222/104
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 74/84,156/27,222/104, numerators are 74,156,222
Denominators are 84,27,104
The GCF of 74,156,222 is 2 .
LCM of 84,27,104 is 19656.
The greatest common factor of 74/84,156/27,222/104 = [GCF of 74,156,222]/[LCM of 84,27,104]= 2/19656
Therefore, the GCF of 74/84,156/27,222/104 is 2/19656.
To find the highest common factor of 74,156,222, we have to find the factors of both numbers and list the highest common factor.
The factors of 74 are 1, 2, 37, 74
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The HCF of 74,156,222 is 2.
Lets's calculate GCF of 74,156,222
2 | 74, 156, 222 |
37, 78, 111 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Greatest Common Factor
We found the factors 74,156,222 . The biggest common factor number is the GCF number.
So the greatest common factor 74,156,222 is 2.
Lets's calculate LCM of 84,27,104
2 | 84, 27, 104 |
2 | 42, 27, 52 |
3 | 21, 27, 26 |
7, 9, 26 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 9 x 26 = 19656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/19656
Therefore, the GCF of Fractions 74/84,156/27,222/104 is 2/19656
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 84,27,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,27,104) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(84,27,104) x common factors =1 x 12 = 12
LCM(84,27,104) = ( 84 × 27 × 104 ) / 12
LCM(84,27,104) = 235872 / 12
LCM(84,27,104) = 19656
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 74,156,222?
The HCF of 74,156,222 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 74/84, 156/27, 222/104?
Answer: GCF of Numerators as per given numbers 74/84, 156/27, 222/104 is
GCF of Numerators i.e. for 74,156,222 is 2
LCM of denominators i.e. for 84,27,104 is 19656.
Thus, GCF of Fractions is 2/19656.Finally, GCF of Fractions for 74/84, 156/27, 222/104 is 2/19656.