GCF of 310/231, 3069/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 310/231, 3069/312 i.e 31/24024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/231, 3069/312.
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 310/231,3069/312?
Given fractions are 310/231,3069/312
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 310/231,3069/312, numerators are 310,3069
Denominators are 231,312
The GCF of 310,3069 is 31 .
LCM of 231,312 is 24024.
The greatest common factor of 310/231,3069/312 = [GCF of 310,3069]/[LCM of 231,312]= 31/24024
Therefore, the GCF of 310/231,3069/312 is 31/24024.
To find the highest common factor of 310,3069, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 3069 are 1, 3, 9, 11, 31, 33, 93, 99, 279, 341, 1023, 3069
The HCF of 310,3069 is 31.
Lets's calculate GCF of 310,3069
| 31 | 310, 3069 |
| 10, 99 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 310,3069 By Matching Biggest Common Factor Method
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 3069
:1,3,9,11,31,33,93,99,279,341,1023,3069
Greatest Common Factor
We found the factors 310,3069 . The biggest common factor number is the GCF number.
So the greatest common factor 310,3069 is 31.
Lets's calculate LCM of 231,312
| 3 | 231, 312 |
| 77, 104 |
∴ So the LCM of the given numbers is 3 x 77 x 104 = 24024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/24024
Therefore, the GCF of Fractions 310/231,3069/312 is 31/24024
Least Common Multiple of 231,312 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 231,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(231,312) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(231,312) x common factors =3 x 1 = 3
LCM(231,312) = ( 231 × 312 ) / 3
LCM(231,312) = 72072 / 3
LCM(231,312) = 24024
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FAQs on GCF of Fractions of 310/231, 3069/312
1. What is the HCF of 310,3069?
The HCF of 310,3069 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 310/231, 3069/312?
Answer: GCF of Numerators as per given numbers 310/231, 3069/312 is
GCF of Numerators i.e. for 310,3069 is 31
LCM of denominators i.e. for 231,312 is 24024.
Thus, GCF of Fractions is 31/24024.Finally, GCF of Fractions for 310/231, 3069/312 is 31/24024.