GCF of 189/428, 7314/953
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 189/428, 7314/953 i.e 3/407884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/428, 7314/953.
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 189/428,7314/953?
Given fractions are 189/428,7314/953
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 189/428,7314/953, numerators are 189,7314
Denominators are 428,953
The GCF of 189,7314 is 3 .
LCM of 428,953 is 407884.
The greatest common factor of 189/428,7314/953 = [GCF of 189,7314]/[LCM of 428,953]= 3/407884
Therefore, the GCF of 189/428,7314/953 is 3/407884.
To find the highest common factor of 189,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 189,7314 is 3.
Lets's calculate GCF of 189,7314
| 3 | 189, 7314 |
| 63, 2438 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 189,7314 By Matching Biggest Common Factor Method
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 189,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 189,7314 is 3.
Lets's calculate LCM of 428,953
Given numbers has no common factors except 1. So, there LCM is their product i.e 407884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/407884
Therefore, the GCF of Fractions 189/428,7314/953 is 3/407884
Least Common Multiple of 428,953 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 428,953 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(428,953) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(428,953) x common factors =1 x 1 = 1
LCM(428,953) = ( 428 × 953 ) / 1
LCM(428,953) = 407884 / 1
LCM(428,953) = 407884
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FAQs on GCF of Fractions of 189/428, 7314/953
1. What is the HCF of 189,7314?
The HCF of 189,7314 is 3
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 189/428, 7314/953?
Answer: GCF of Numerators as per given numbers 189/428, 7314/953 is
GCF of Numerators i.e. for 189,7314 is 3
LCM of denominators i.e. for 428,953 is 407884.
Thus, GCF of Fractions is 3/407884.Finally, GCF of Fractions for 189/428, 7314/953 is 3/407884.