Use our free GCF of Fractions Calculator tool to compute the GCF of 34/77, 42/99, 91/84, 32/41 i.e 1/113652 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/77, 42/99, 91/84, 32/41.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/77,42/99,91/84,32/41
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 34/77,42/99,91/84,32/41, numerators are 34,42,91,32
Denominators are 77,99,84,41
The GCF of 34,42,91,32 is 1 .
LCM of 77,99,84,41 is 113652.
The greatest common factor of 34/77,42/99,91/84,32/41 = [GCF of 34,42,91,32]/[LCM of 77,99,84,41]= 1/113652
Therefore, the GCF of 34/77,42/99,91/84,32/41 is 1/113652.
To find the highest common factor of 34,42,91,32, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 91 are 1, 7, 13, 91
The factors of 32 are 1, 2, 4, 8, 16, 32
The HCF of 34,42,91,32 is 1.
Lets's calculate GCF of 34,42,91,32
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 91
:1,7,13,91
Now, list down the factors of 32
:1,2,4,8,16,32
Greatest Common Factor
We found the factors 34,42,91,32 . The biggest common factor number is the GCF number.
So the greatest common factor 34,42,91,32 is 1.
Lets's calculate LCM of 77,99,84,41
3 | 77, 99, 84, 41 |
7 | 77, 33, 28, 41 |
11 | 11, 33, 4, 41 |
1, 3, 4, 41 |
∴ So the LCM of the given numbers is 3 x 7 x 11 x 1 x 3 x 4 x 41 = 113652
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/113652
Therefore, the GCF of Fractions 34/77,42/99,91/84,32/41 is 1/113652
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 77,99,84,41 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,99,84,41) = 1
common factors(in case of two or more numbers have common factors) = 231
GCF(77,99,84,41) x common factors =1 x 231 = 231
LCM(77,99,84,41) = ( 77 × 99 × 84 × 41 ) / 231
LCM(77,99,84,41) = 26253612 / 231
LCM(77,99,84,41) = 113652
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 34,42,91,32?
The HCF of 34,42,91,32 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 34/77, 42/99, 91/84, 32/41?
Answer: GCF of Numerators as per given numbers 34/77, 42/99, 91/84, 32/41 is
GCF of Numerators i.e. for 34,42,91,32 is 1
LCM of denominators i.e. for 77,99,84,41 is 113652.
Thus, GCF of Fractions is 1/113652.Finally, GCF of Fractions for 34/77, 42/99, 91/84, 32/41 is 1/113652.