GCF of 182/54, 312/137
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 182/54, 312/137 i.e 26/7398 easily. The following is the detailed procedure to determine the greatest common factor of fractions 182/54, 312/137.
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 182/54,312/137?
Given fractions are 182/54,312/137
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 182/54,312/137, numerators are 182,312
Denominators are 54,137
The GCF of 182,312 is 26 .
LCM of 54,137 is 7398.
The greatest common factor of 182/54,312/137 = [GCF of 182,312]/[LCM of 54,137]= 26/7398
Therefore, the GCF of 182/54,312/137 is 26/7398.
To find the highest common factor of 182,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 182,312 is 26.
Lets's calculate GCF of 182,312
| 2 | 182, 312 |
| 13 | 91, 156 |
| 7, 12 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 182,312 By Matching Biggest Common Factor Method
Now, list down the factors of 182
:1,2,7,13,14,26,91,182
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 182,312 . The biggest common factor number is the GCF number.
So the greatest common factor 182,312 is 26.
Lets's calculate LCM of 54,137
Given numbers has no common factors except 1. So, there LCM is their product i.e 7398
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/7398
Therefore, the GCF of Fractions 182/54,312/137 is 26/7398
Least Common Multiple of 54,137 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 54,137 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,137) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(54,137) x common factors =1 x 1 = 1
LCM(54,137) = ( 54 × 137 ) / 1
LCM(54,137) = 7398 / 1
LCM(54,137) = 7398
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 182/54, 312/137
1. What is the HCF of 182,312?
The HCF of 182,312 is 26
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 182/54, 312/137?
Answer: GCF of Numerators as per given numbers 182/54, 312/137 is
GCF of Numerators i.e. for 182,312 is 26
LCM of denominators i.e. for 54,137 is 7398.
Thus, GCF of Fractions is 26/7398.Finally, GCF of Fractions for 182/54, 312/137 is 26/7398.