GCF of 364/66, 269/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 364/66, 269/174 i.e 1/1914 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/66, 269/174.
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 364/66,269/174?
Given fractions are 364/66,269/174
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 364/66,269/174, numerators are 364,269
Denominators are 66,174
The GCF of 364,269 is 1 .
LCM of 66,174 is 1914.
The greatest common factor of 364/66,269/174 = [GCF of 364,269]/[LCM of 66,174]= 1/1914
Therefore, the GCF of 364/66,269/174 is 1/1914.
To find the highest common factor of 364,269, we have to find the factors of both numbers and list the highest common factor.
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The factors of 269 are 1, 269
The HCF of 364,269 is 1.
Lets's calculate GCF of 364,269
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 364,269 By Matching Biggest Common Factor Method
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Now, list down the factors of 269
:1,269
Greatest Common Factor
We found the factors 364,269 . The biggest common factor number is the GCF number.
So the greatest common factor 364,269 is 1.
Lets's calculate LCM of 66,174
| 2 | 66, 174 |
| 3 | 33, 87 |
| 11, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 29 = 1914
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1914
Therefore, the GCF of Fractions 364/66,269/174 is 1/1914
Least Common Multiple of 66,174 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 66,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,174) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(66,174) x common factors =6 x 1 = 6
LCM(66,174) = ( 66 × 174 ) / 6
LCM(66,174) = 11484 / 6
LCM(66,174) = 1914
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 364/66, 269/174
1. What is the HCF of 364,269?
The HCF of 364,269 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 364/66, 269/174?
Answer: GCF of Numerators as per given numbers 364/66, 269/174 is
GCF of Numerators i.e. for 364,269 is 1
LCM of denominators i.e. for 66,174 is 1914.
Thus, GCF of Fractions is 1/1914.Finally, GCF of Fractions for 364/66, 269/174 is 1/1914.