Use our free GCF of Fractions Calculator tool to compute the GCF of 7/51, 34/86, 45/120, 945/735 i.e 1/4298280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/51, 34/86, 45/120, 945/735.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7/51,34/86,45/120,945/735
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 7/51,34/86,45/120,945/735, numerators are 7,34,45,945
Denominators are 51,86,120,735
The GCF of 7,34,45,945 is 1 .
LCM of 51,86,120,735 is 4298280.
The greatest common factor of 7/51,34/86,45/120,945/735 = [GCF of 7,34,45,945]/[LCM of 51,86,120,735]= 1/4298280
Therefore, the GCF of 7/51,34/86,45/120,945/735 is 1/4298280.
To find the highest common factor of 7,34,45,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 7 are 1, 7
The factors of 34 are 1, 2, 17, 34
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 7,34,45,945 is 1.
Lets's calculate GCF of 7,34,45,945
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 7
:1,7
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 7,34,45,945 . The biggest common factor number is the GCF number.
So the greatest common factor 7,34,45,945 is 1.
Lets's calculate LCM of 51,86,120,735
2 | 51, 86, 120, 735 |
3 | 51, 43, 60, 735 |
5 | 17, 43, 20, 245 |
17, 43, 4, 49 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 17 x 43 x 4 x 49 = 4298280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4298280
Therefore, the GCF of Fractions 7/51,34/86,45/120,945/735 is 1/4298280
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 51,86,120,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,86,120,735) = 1
common factors(in case of two or more numbers have common factors) = 90
GCF(51,86,120,735) x common factors =1 x 90 = 90
LCM(51,86,120,735) = ( 51 × 86 × 120 × 735 ) / 90
LCM(51,86,120,735) = 386845200 / 90
LCM(51,86,120,735) = 4298280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7,34,45,945?
The HCF of 7,34,45,945 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 7/51, 34/86, 45/120, 945/735?
Answer: GCF of Numerators as per given numbers 7/51, 34/86, 45/120, 945/735 is
GCF of Numerators i.e. for 7,34,45,945 is 1
LCM of denominators i.e. for 51,86,120,735 is 4298280.
Thus, GCF of Fractions is 1/4298280.Finally, GCF of Fractions for 7/51, 34/86, 45/120, 945/735 is 1/4298280.