GCF of 323/320, 7140/501
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 323/320, 7140/501 i.e 17/160320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 323/320, 7140/501.
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 323/320,7140/501?
Given fractions are 323/320,7140/501
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 323/320,7140/501, numerators are 323,7140
Denominators are 320,501
The GCF of 323,7140 is 17 .
LCM of 320,501 is 160320.
The greatest common factor of 323/320,7140/501 = [GCF of 323,7140]/[LCM of 320,501]= 17/160320
Therefore, the GCF of 323/320,7140/501 is 17/160320.
To find the highest common factor of 323,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 323 are 1, 17, 19, 323
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The HCF of 323,7140 is 17.
Lets's calculate GCF of 323,7140
| 17 | 323, 7140 |
| 19, 420 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 323,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 323
:1,17,19,323
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Greatest Common Factor
We found the factors 323,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 323,7140 is 17.
Lets's calculate LCM of 320,501
Given numbers has no common factors except 1. So, there LCM is their product i.e 160320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/160320
Therefore, the GCF of Fractions 323/320,7140/501 is 17/160320
Least Common Multiple of 320,501 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 320,501 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,501) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(320,501) x common factors =1 x 1 = 1
LCM(320,501) = ( 320 × 501 ) / 1
LCM(320,501) = 160320 / 1
LCM(320,501) = 160320
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FAQs on GCF of Fractions of 323/320, 7140/501
1. What is the HCF of 323,7140?
The HCF of 323,7140 is 17
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 323/320, 7140/501?
Answer: GCF of Numerators as per given numbers 323/320, 7140/501 is
GCF of Numerators i.e. for 323,7140 is 17
LCM of denominators i.e. for 320,501 is 160320.
Thus, GCF of Fractions is 17/160320.Finally, GCF of Fractions for 323/320, 7140/501 is 17/160320.