Use our free GCF of Fractions Calculator tool to compute the GCF of 52/24, 221/35, 108/704 i.e 1/73920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 52/24, 221/35, 108/704.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 52/24,221/35,108/704
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 52/24,221/35,108/704, numerators are 52,221,108
Denominators are 24,35,704
The GCF of 52,221,108 is 1 .
LCM of 24,35,704 is 73920.
The greatest common factor of 52/24,221/35,108/704 = [GCF of 52,221,108]/[LCM of 24,35,704]= 1/73920
Therefore, the GCF of 52/24,221/35,108/704 is 1/73920.
To find the highest common factor of 52,221,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 221 are 1, 13, 17, 221
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 52,221,108 is 1.
Lets's calculate GCF of 52,221,108
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 221
:1,13,17,221
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 52,221,108 . The biggest common factor number is the GCF number.
So the greatest common factor 52,221,108 is 1.
Lets's calculate LCM of 24,35,704
2 | 24, 35, 704 |
2 | 12, 35, 352 |
2 | 6, 35, 176 |
3, 35, 88 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 35 x 88 = 73920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73920
Therefore, the GCF of Fractions 52/24,221/35,108/704 is 1/73920
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 24,35,704 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,35,704) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(24,35,704) x common factors =1 x 8 = 8
LCM(24,35,704) = ( 24 × 35 × 704 ) / 8
LCM(24,35,704) = 591360 / 8
LCM(24,35,704) = 73920
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 52,221,108?
The HCF of 52,221,108 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 52/24, 221/35, 108/704?
Answer: GCF of Numerators as per given numbers 52/24, 221/35, 108/704 is
GCF of Numerators i.e. for 52,221,108 is 1
LCM of denominators i.e. for 24,35,704 is 73920.
Thus, GCF of Fractions is 1/73920.Finally, GCF of Fractions for 52/24, 221/35, 108/704 is 1/73920.