GCF of 745/188, 975/114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 745/188, 975/114 i.e 5/10716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 745/188, 975/114.
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 745/188,975/114?
Given fractions are 745/188,975/114
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 745/188,975/114, numerators are 745,975
Denominators are 188,114
The GCF of 745,975 is 5 .
LCM of 188,114 is 10716.
The greatest common factor of 745/188,975/114 = [GCF of 745,975]/[LCM of 188,114]= 5/10716
Therefore, the GCF of 745/188,975/114 is 5/10716.
To find the highest common factor of 745,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 745 are 1, 5, 149, 745
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 745,975 is 5.
Lets's calculate GCF of 745,975
| 5 | 745, 975 |
| 149, 195 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 745,975 By Matching Biggest Common Factor Method
Now, list down the factors of 745
:1,5,149,745
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 745,975 . The biggest common factor number is the GCF number.
So the greatest common factor 745,975 is 5.
Lets's calculate LCM of 188,114
| 2 | 188, 114 |
| 94, 57 |
∴ So the LCM of the given numbers is 2 x 94 x 57 = 10716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/10716
Therefore, the GCF of Fractions 745/188,975/114 is 5/10716
Least Common Multiple of 188,114 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 188,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,114) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(188,114) x common factors =2 x 1 = 2
LCM(188,114) = ( 188 × 114 ) / 2
LCM(188,114) = 21432 / 2
LCM(188,114) = 10716
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FAQs on GCF of Fractions of 745/188, 975/114
1. What is the HCF of 745,975?
The HCF of 745,975 is 5
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 745/188, 975/114?
Answer: GCF of Numerators as per given numbers 745/188, 975/114 is
GCF of Numerators i.e. for 745,975 is 5
LCM of denominators i.e. for 188,114 is 10716.
Thus, GCF of Fractions is 5/10716.Finally, GCF of Fractions for 745/188, 975/114 is 5/10716.