GCF of 230/12, 772/31, 106/65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 230/12, 772/31, 106/65 i.e 2/24180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 230/12, 772/31, 106/65.
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 230/12,772/31,106/65?
Given fractions are 230/12,772/31,106/65
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 230/12,772/31,106/65, numerators are 230,772,106
Denominators are 12,31,65
The GCF of 230,772,106 is 2 .
LCM of 12,31,65 is 24180.
The greatest common factor of 230/12,772/31,106/65 = [GCF of 230,772,106]/[LCM of 12,31,65]= 2/24180
Therefore, the GCF of 230/12,772/31,106/65 is 2/24180.
To find the highest common factor of 230,772,106, we have to find the factors of both numbers and list the highest common factor.
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230
The factors of 772 are 1, 2, 4, 193, 386, 772
The factors of 106 are 1, 2, 53, 106
The HCF of 230,772,106 is 2.
Lets's calculate GCF of 230,772,106
| 2 | 230, 772, 106 |
| 115, 386, 53 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 230,772,106 By Matching Biggest Common Factor Method
Now, list down the factors of 230
:1,2,5,10,23,46,115,230
Now, list down the factors of 772
:1,2,4,193,386,772
Now, list down the factors of 106
:1,2,53,106
Greatest Common Factor
We found the factors 230,772,106 . The biggest common factor number is the GCF number.
So the greatest common factor 230,772,106 is 2.
Lets's calculate LCM of 12,31,65
Given numbers has no common factors except 1. So, there LCM is their product i.e 24180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/24180
Therefore, the GCF of Fractions 230/12,772/31,106/65 is 2/24180
Least Common Multiple of 12,31,65 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 12,31,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,31,65) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(12,31,65) x common factors =1 x 1 = 1
LCM(12,31,65) = ( 12 × 31 × 65 ) / 1
LCM(12,31,65) = 24180 / 1
LCM(12,31,65) = 24180
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FAQs on GCF of Fractions of 230/12, 772/31, 106/65
1. What is the HCF of 230,772,106?
The HCF of 230,772,106 is 2
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 230/12, 772/31, 106/65?
Answer: GCF of Numerators as per given numbers 230/12, 772/31, 106/65 is
GCF of Numerators i.e. for 230,772,106 is 2
LCM of denominators i.e. for 12,31,65 is 24180.
Thus, GCF of Fractions is 2/24180.Finally, GCF of Fractions for 230/12, 772/31, 106/65 is 2/24180.