GCF of 3131/763, 7409/422
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3131/763, 7409/422 i.e 31/321986 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3131/763, 7409/422.
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 3131/763,7409/422?
Given fractions are 3131/763,7409/422
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 3131/763,7409/422, numerators are 3131,7409
Denominators are 763,422
The GCF of 3131,7409 is 31 .
LCM of 763,422 is 321986.
The greatest common factor of 3131/763,7409/422 = [GCF of 3131,7409]/[LCM of 763,422]= 31/321986
Therefore, the GCF of 3131/763,7409/422 is 31/321986.
To find the highest common factor of 3131,7409, we have to find the factors of both numbers and list the highest common factor.
The factors of 3131 are 1, 31, 101, 3131
The factors of 7409 are 1, 31, 239, 7409
The HCF of 3131,7409 is 31.
Lets's calculate GCF of 3131,7409
| 31 | 3131, 7409 |
| 101, 239 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 3131,7409 By Matching Biggest Common Factor Method
Now, list down the factors of 3131
:1,31,101,3131
Now, list down the factors of 7409
:1,31,239,7409
Greatest Common Factor
We found the factors 3131,7409 . The biggest common factor number is the GCF number.
So the greatest common factor 3131,7409 is 31.
Lets's calculate LCM of 763,422
Given numbers has no common factors except 1. So, there LCM is their product i.e 321986
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/321986
Therefore, the GCF of Fractions 3131/763,7409/422 is 31/321986
Least Common Multiple of 763,422 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 763,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(763,422) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(763,422) x common factors =1 x 1 = 1
LCM(763,422) = ( 763 × 422 ) / 1
LCM(763,422) = 321986 / 1
LCM(763,422) = 321986
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FAQs on GCF of Fractions of 3131/763, 7409/422
1. What is the HCF of 3131,7409?
The HCF of 3131,7409 is 31
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 3131/763, 7409/422?
Answer: GCF of Numerators as per given numbers 3131/763, 7409/422 is
GCF of Numerators i.e. for 3131,7409 is 31
LCM of denominators i.e. for 763,422 is 321986.
Thus, GCF of Fractions is 31/321986.Finally, GCF of Fractions for 3131/763, 7409/422 is 31/321986.