Use our free GCF of Fractions Calculator tool to compute the GCF of 29/617, 37/106, 234/704 i.e 1/23021504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/617, 37/106, 234/704.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 29/617,37/106,234/704
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 29/617,37/106,234/704, numerators are 29,37,234
Denominators are 617,106,704
The GCF of 29,37,234 is 1 .
LCM of 617,106,704 is 23021504.
The greatest common factor of 29/617,37/106,234/704 = [GCF of 29,37,234]/[LCM of 617,106,704]= 1/23021504
Therefore, the GCF of 29/617,37/106,234/704 is 1/23021504.
To find the highest common factor of 29,37,234, we have to find the factors of both numbers and list the highest common factor.
The factors of 29 are 1, 29
The factors of 37 are 1, 37
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The HCF of 29,37,234 is 1.
Lets's calculate GCF of 29,37,234
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 29
:1,29
Now, list down the factors of 37
:1,37
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Greatest Common Factor
We found the factors 29,37,234 . The biggest common factor number is the GCF number.
So the greatest common factor 29,37,234 is 1.
Lets's calculate LCM of 617,106,704
2 | 617, 106, 704 |
617, 53, 352 |
∴ So the LCM of the given numbers is 2 x 617 x 53 x 352 = 23021504
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23021504
Therefore, the GCF of Fractions 29/617,37/106,234/704 is 1/23021504
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 617,106,704 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(617,106,704) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(617,106,704) x common factors =1 x 2 = 2
LCM(617,106,704) = ( 617 × 106 × 704 ) / 2
LCM(617,106,704) = 46043008 / 2
LCM(617,106,704) = 23021504
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 29,37,234?
The HCF of 29,37,234 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 29/617, 37/106, 234/704?
Answer: GCF of Numerators as per given numbers 29/617, 37/106, 234/704 is
GCF of Numerators i.e. for 29,37,234 is 1
LCM of denominators i.e. for 617,106,704 is 23021504.
Thus, GCF of Fractions is 1/23021504.Finally, GCF of Fractions for 29/617, 37/106, 234/704 is 1/23021504.