Use our free GCF of Fractions Calculator tool to compute the GCF of 21/75, 56/32, 707/40 i.e 7/2400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/75, 56/32, 707/40.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/75,56/32,707/40
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 21/75,56/32,707/40, numerators are 21,56,707
Denominators are 75,32,40
The GCF of 21,56,707 is 7 .
LCM of 75,32,40 is 2400.
The greatest common factor of 21/75,56/32,707/40 = [GCF of 21,56,707]/[LCM of 75,32,40]= 7/2400
Therefore, the GCF of 21/75,56/32,707/40 is 7/2400.
To find the highest common factor of 21,56,707, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 707 are 1, 7, 101, 707
The HCF of 21,56,707 is 7.
Lets's calculate GCF of 21,56,707
7 | 21, 56, 707 |
3, 8, 101 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 707
:1,7,101,707
Greatest Common Factor
We found the factors 21,56,707 . The biggest common factor number is the GCF number.
So the greatest common factor 21,56,707 is 7.
Lets's calculate LCM of 75,32,40
2 | 75, 32, 40 |
2 | 75, 16, 20 |
2 | 75, 8, 10 |
5 | 75, 4, 5 |
15, 4, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 15 x 4 x 1 = 2400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/2400
Therefore, the GCF of Fractions 21/75,56/32,707/40 is 7/2400
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 75,32,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,32,40) = 1
common factors(in case of two or more numbers have common factors) = 40
GCF(75,32,40) x common factors =1 x 40 = 40
LCM(75,32,40) = ( 75 × 32 × 40 ) / 40
LCM(75,32,40) = 96000 / 40
LCM(75,32,40) = 2400
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,56,707?
The HCF of 21,56,707 is 7
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 21/75, 56/32, 707/40?
Answer: GCF of Numerators as per given numbers 21/75, 56/32, 707/40 is
GCF of Numerators i.e. for 21,56,707 is 7
LCM of denominators i.e. for 75,32,40 is 2400.
Thus, GCF of Fractions is 7/2400.Finally, GCF of Fractions for 21/75, 56/32, 707/40 is 7/2400.