GCF of 75/19, 69/51, 60/56, 44/153
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/19, 69/51, 60/56, 44/153 i.e 1/162792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/19, 69/51, 60/56, 44/153.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 75/19,69/51,60/56,44/153?
Given fractions are 75/19,69/51,60/56,44/153
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 75/19,69/51,60/56,44/153, numerators are 75,69,60,44
Denominators are 19,51,56,153
The GCF of 75,69,60,44 is 1 .
LCM of 19,51,56,153 is 162792.
The greatest common factor of 75/19,69/51,60/56,44/153 = [GCF of 75,69,60,44]/[LCM of 19,51,56,153]= 1/162792
Therefore, the GCF of 75/19,69/51,60/56,44/153 is 1/162792.
To find the highest common factor of 75,69,60,44, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 69 are 1, 3, 23, 69
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 44 are 1, 2, 4, 11, 22, 44
The HCF of 75,69,60,44 is 1.
Lets's calculate GCF of 75,69,60,44
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 75,69,60,44 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 44
:1,2,4,11,22,44
Greatest Common Factor
We found the factors 75,69,60,44 . The biggest common factor number is the GCF number.
So the greatest common factor 75,69,60,44 is 1.
Lets's calculate LCM of 19,51,56,153
| 3 | 19, 51, 56, 153 |
| 17 | 19, 17, 56, 51 |
| 19, 1, 56, 3 |
∴ So the LCM of the given numbers is 3 x 17 x 19 x 1 x 56 x 3 = 162792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/162792
Therefore, the GCF of Fractions 75/19,69/51,60/56,44/153 is 1/162792
Least Common Multiple of 19,51,56,153 with GCF Formula
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 19,51,56,153 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,51,56,153) = 1
common factors(in case of two or more numbers have common factors) = 51
GCF(19,51,56,153) x common factors =1 x 51 = 51
LCM(19,51,56,153) = ( 19 × 51 × 56 × 153 ) / 51
LCM(19,51,56,153) = 8302392 / 51
LCM(19,51,56,153) = 162792
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 75/19, 69/51, 60/56, 44/153
1. What is the HCF of 75,69,60,44?
The HCF of 75,69,60,44 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 75/19, 69/51, 60/56, 44/153?
Answer: GCF of Numerators as per given numbers 75/19, 69/51, 60/56, 44/153 is
GCF of Numerators i.e. for 75,69,60,44 is 1
LCM of denominators i.e. for 19,51,56,153 is 162792.
Thus, GCF of Fractions is 1/162792.Finally, GCF of Fractions for 75/19, 69/51, 60/56, 44/153 is 1/162792.