GCF of 51/12, 31/34, 32/46, 19/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 51/12, 31/34, 32/46, 19/31 i.e 1/145452 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/12, 31/34, 32/46, 19/31.
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 51/12,31/34,32/46,19/31?
Given fractions are 51/12,31/34,32/46,19/31
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 51/12,31/34,32/46,19/31, numerators are 51,31,32,19
Denominators are 12,34,46,31
The GCF of 51,31,32,19 is 1 .
LCM of 12,34,46,31 is 145452.
The greatest common factor of 51/12,31/34,32/46,19/31 = [GCF of 51,31,32,19]/[LCM of 12,34,46,31]= 1/145452
Therefore, the GCF of 51/12,31/34,32/46,19/31 is 1/145452.
To find the highest common factor of 51,31,32,19, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 31 are 1, 31
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 19 are 1, 19
The HCF of 51,31,32,19 is 1.
Lets's calculate GCF of 51,31,32,19
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 51,31,32,19 By Matching Biggest Common Factor Method
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 31
:1,31
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 19
:1,19
Greatest Common Factor
We found the factors 51,31,32,19 . The biggest common factor number is the GCF number.
So the greatest common factor 51,31,32,19 is 1.
Lets's calculate LCM of 12,34,46,31
| 2 | 12, 34, 46, 31 |
| 6, 17, 23, 31 |
∴ So the LCM of the given numbers is 2 x 6 x 17 x 23 x 31 = 145452
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/145452
Therefore, the GCF of Fractions 51/12,31/34,32/46,19/31 is 1/145452
Least Common Multiple of 12,34,46,31 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 12,34,46,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,34,46,31) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(12,34,46,31) x common factors =1 x 4 = 4
LCM(12,34,46,31) = ( 12 × 34 × 46 × 31 ) / 4
LCM(12,34,46,31) = 581808 / 4
LCM(12,34,46,31) = 145452
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 51/12, 31/34, 32/46, 19/31
1. What is the HCF of 51,31,32,19?
The HCF of 51,31,32,19 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 51/12, 31/34, 32/46, 19/31?
Answer: GCF of Numerators as per given numbers 51/12, 31/34, 32/46, 19/31 is
GCF of Numerators i.e. for 51,31,32,19 is 1
LCM of denominators i.e. for 12,34,46,31 is 145452.
Thus, GCF of Fractions is 1/145452.Finally, GCF of Fractions for 51/12, 31/34, 32/46, 19/31 is 1/145452.