GCF of 171/78, 976/2014
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 171/78, 976/2014 i.e 1/78546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 171/78, 976/2014.
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 171/78,976/2014?
Given fractions are 171/78,976/2014
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 171/78,976/2014, numerators are 171,976
Denominators are 78,2014
The GCF of 171,976 is 1 .
LCM of 78,2014 is 78546.
The greatest common factor of 171/78,976/2014 = [GCF of 171,976]/[LCM of 78,2014]= 1/78546
Therefore, the GCF of 171/78,976/2014 is 1/78546.
To find the highest common factor of 171,976, we have to find the factors of both numbers and list the highest common factor.
The factors of 171 are 1, 3, 9, 19, 57, 171
The factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976
The HCF of 171,976 is 1.
Lets's calculate GCF of 171,976
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 171,976 By Matching Biggest Common Factor Method
Now, list down the factors of 171
:1,3,9,19,57,171
Now, list down the factors of 976
:1,2,4,8,16,61,122,244,488,976
Greatest Common Factor
We found the factors 171,976 . The biggest common factor number is the GCF number.
So the greatest common factor 171,976 is 1.
Lets's calculate LCM of 78,2014
| 2 | 78, 2014 |
| 39, 1007 |
∴ So the LCM of the given numbers is 2 x 39 x 1007 = 78546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/78546
Therefore, the GCF of Fractions 171/78,976/2014 is 1/78546
Least Common Multiple of 78,2014 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 78,2014 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,2014) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(78,2014) x common factors =2 x 1 = 2
LCM(78,2014) = ( 78 × 2014 ) / 2
LCM(78,2014) = 157092 / 2
LCM(78,2014) = 78546
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FAQs on GCF of Fractions of 171/78, 976/2014
1. What is the HCF of 171,976?
The HCF of 171,976 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 171/78, 976/2014?
Answer: GCF of Numerators as per given numbers 171/78, 976/2014 is
GCF of Numerators i.e. for 171,976 is 1
LCM of denominators i.e. for 78,2014 is 78546.
Thus, GCF of Fractions is 1/78546.Finally, GCF of Fractions for 171/78, 976/2014 is 1/78546.