GCF of 183/77, 678/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 183/77, 678/129 i.e 3/9933 easily. The following is the detailed procedure to determine the greatest common factor of fractions 183/77, 678/129.
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 183/77,678/129?
Given fractions are 183/77,678/129
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 183/77,678/129, numerators are 183,678
Denominators are 77,129
The GCF of 183,678 is 3 .
LCM of 77,129 is 9933.
The greatest common factor of 183/77,678/129 = [GCF of 183,678]/[LCM of 77,129]= 3/9933
Therefore, the GCF of 183/77,678/129 is 3/9933.
To find the highest common factor of 183,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 183 are 1, 3, 61, 183
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 183,678 is 3.
Lets's calculate GCF of 183,678
| 3 | 183, 678 |
| 61, 226 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 183,678 By Matching Biggest Common Factor Method
Now, list down the factors of 183
:1,3,61,183
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 183,678 . The biggest common factor number is the GCF number.
So the greatest common factor 183,678 is 3.
Lets's calculate LCM of 77,129
Given numbers has no common factors except 1. So, there LCM is their product i.e 9933
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/9933
Therefore, the GCF of Fractions 183/77,678/129 is 3/9933
Least Common Multiple of 77,129 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 77,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,129) x common factors =1 x 1 = 1
LCM(77,129) = ( 77 × 129 ) / 1
LCM(77,129) = 9933 / 1
LCM(77,129) = 9933
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FAQs on GCF of Fractions of 183/77, 678/129
1. What is the HCF of 183,678?
The HCF of 183,678 is 3
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 183/77, 678/129?
Answer: GCF of Numerators as per given numbers 183/77, 678/129 is
GCF of Numerators i.e. for 183,678 is 3
LCM of denominators i.e. for 77,129 is 9933.
Thus, GCF of Fractions is 3/9933.Finally, GCF of Fractions for 183/77, 678/129 is 3/9933.