GCF of 277/324, 284/342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 277/324, 284/342 i.e 1/6156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 277/324, 284/342.
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 277/324,284/342?
Given fractions are 277/324,284/342
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 277/324,284/342, numerators are 277,284
Denominators are 324,342
The GCF of 277,284 is 1 .
LCM of 324,342 is 6156.
The greatest common factor of 277/324,284/342 = [GCF of 277,284]/[LCM of 324,342]= 1/6156
Therefore, the GCF of 277/324,284/342 is 1/6156.
To find the highest common factor of 277,284, we have to find the factors of both numbers and list the highest common factor.
The factors of 277 are 1, 277
The factors of 284 are 1, 2, 4, 71, 142, 284
The HCF of 277,284 is 1.
Lets's calculate GCF of 277,284
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 277,284 By Matching Biggest Common Factor Method
Now, list down the factors of 277
:1,277
Now, list down the factors of 284
:1,2,4,71,142,284
Greatest Common Factor
We found the factors 277,284 . The biggest common factor number is the GCF number.
So the greatest common factor 277,284 is 1.
Lets's calculate LCM of 324,342
| 2 | 324, 342 |
| 3 | 162, 171 |
| 3 | 54, 57 |
| 18, 19 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 18 x 19 = 6156
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6156
Therefore, the GCF of Fractions 277/324,284/342 is 1/6156
Least Common Multiple of 324,342 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 324,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,342) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(324,342) x common factors =18 x 1 = 18
LCM(324,342) = ( 324 × 342 ) / 18
LCM(324,342) = 110808 / 18
LCM(324,342) = 6156
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FAQs on GCF of Fractions of 277/324, 284/342
1. What is the HCF of 277,284?
The HCF of 277,284 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 277/324, 284/342?
Answer: GCF of Numerators as per given numbers 277/324, 284/342 is
GCF of Numerators i.e. for 277,284 is 1
LCM of denominators i.e. for 324,342 is 6156.
Thus, GCF of Fractions is 1/6156.Finally, GCF of Fractions for 277/324, 284/342 is 1/6156.