GCF of 975/277, 169/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 975/277, 169/174 i.e 13/48198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/277, 169/174.
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 975/277,169/174?
Given fractions are 975/277,169/174
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 975/277,169/174, numerators are 975,169
Denominators are 277,174
The GCF of 975,169 is 13 .
LCM of 277,174 is 48198.
The greatest common factor of 975/277,169/174 = [GCF of 975,169]/[LCM of 277,174]= 13/48198
Therefore, the GCF of 975/277,169/174 is 13/48198.
To find the highest common factor of 975,169, we have to find the factors of both numbers and list the highest common factor.
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 169 are 1, 13, 169
The HCF of 975,169 is 13.
Lets's calculate GCF of 975,169
| 13 | 975, 169 |
| 75, 13 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 975,169 By Matching Biggest Common Factor Method
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 169
:1,13,169
Greatest Common Factor
We found the factors 975,169 . The biggest common factor number is the GCF number.
So the greatest common factor 975,169 is 13.
Lets's calculate LCM of 277,174
Given numbers has no common factors except 1. So, there LCM is their product i.e 48198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/48198
Therefore, the GCF of Fractions 975/277,169/174 is 13/48198
Least Common Multiple of 277,174 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 277,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(277,174) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(277,174) x common factors =1 x 1 = 1
LCM(277,174) = ( 277 × 174 ) / 1
LCM(277,174) = 48198 / 1
LCM(277,174) = 48198
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FAQs on GCF of Fractions of 975/277, 169/174
1. What is the HCF of 975,169?
The HCF of 975,169 is 13
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 975/277, 169/174?
Answer: GCF of Numerators as per given numbers 975/277, 169/174 is
GCF of Numerators i.e. for 975,169 is 13
LCM of denominators i.e. for 277,174 is 48198.
Thus, GCF of Fractions is 13/48198.Finally, GCF of Fractions for 975/277, 169/174 is 13/48198.