GCF of 667/17, 184/742
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 667/17, 184/742 i.e 23/12614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 667/17, 184/742.
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 667/17,184/742?
Given fractions are 667/17,184/742
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 667/17,184/742, numerators are 667,184
Denominators are 17,742
The GCF of 667,184 is 23 .
LCM of 17,742 is 12614.
The greatest common factor of 667/17,184/742 = [GCF of 667,184]/[LCM of 17,742]= 23/12614
Therefore, the GCF of 667/17,184/742 is 23/12614.
To find the highest common factor of 667,184, we have to find the factors of both numbers and list the highest common factor.
The factors of 667 are 1, 23, 29, 667
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184
The HCF of 667,184 is 23.
Lets's calculate GCF of 667,184
| 23 | 667, 184 |
| 29, 8 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 667,184 By Matching Biggest Common Factor Method
Now, list down the factors of 667
:1,23,29,667
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Greatest Common Factor
We found the factors 667,184 . The biggest common factor number is the GCF number.
So the greatest common factor 667,184 is 23.
Lets's calculate LCM of 17,742
Given numbers has no common factors except 1. So, there LCM is their product i.e 12614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/12614
Therefore, the GCF of Fractions 667/17,184/742 is 23/12614
Least Common Multiple of 17,742 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 17,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,742) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,742) x common factors =1 x 1 = 1
LCM(17,742) = ( 17 × 742 ) / 1
LCM(17,742) = 12614 / 1
LCM(17,742) = 12614
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FAQs on GCF of Fractions of 667/17, 184/742
1. What is the HCF of 667,184?
The HCF of 667,184 is 23
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 667/17, 184/742?
Answer: GCF of Numerators as per given numbers 667/17, 184/742 is
GCF of Numerators i.e. for 667,184 is 23
LCM of denominators i.e. for 17,742 is 12614.
Thus, GCF of Fractions is 23/12614.Finally, GCF of Fractions for 667/17, 184/742 is 23/12614.