GCF of 140/31, 403/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 140/31, 403/284 i.e 1/8804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 140/31, 403/284.
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 140/31,403/284?
Given fractions are 140/31,403/284
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 140/31,403/284, numerators are 140,403
Denominators are 31,284
The GCF of 140,403 is 1 .
LCM of 31,284 is 8804.
The greatest common factor of 140/31,403/284 = [GCF of 140,403]/[LCM of 31,284]= 1/8804
Therefore, the GCF of 140/31,403/284 is 1/8804.
To find the highest common factor of 140,403, we have to find the factors of both numbers and list the highest common factor.
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The factors of 403 are 1, 13, 31, 403
The HCF of 140,403 is 1.
Lets's calculate GCF of 140,403
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 140,403 By Matching Biggest Common Factor Method
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Now, list down the factors of 403
:1,13,31,403
Greatest Common Factor
We found the factors 140,403 . The biggest common factor number is the GCF number.
So the greatest common factor 140,403 is 1.
Lets's calculate LCM of 31,284
Given numbers has no common factors except 1. So, there LCM is their product i.e 8804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8804
Therefore, the GCF of Fractions 140/31,403/284 is 1/8804
Least Common Multiple of 31,284 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 31,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,284) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,284) x common factors =1 x 1 = 1
LCM(31,284) = ( 31 × 284 ) / 1
LCM(31,284) = 8804 / 1
LCM(31,284) = 8804
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FAQs on GCF of Fractions of 140/31, 403/284
1. What is the HCF of 140,403?
The HCF of 140,403 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 140/31, 403/284?
Answer: GCF of Numerators as per given numbers 140/31, 403/284 is
GCF of Numerators i.e. for 140,403 is 1
LCM of denominators i.e. for 31,284 is 8804.
Thus, GCF of Fractions is 1/8804.Finally, GCF of Fractions for 140/31, 403/284 is 1/8804.