GCF of 678/24, 129/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 678/24, 129/132 i.e 3/264 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/24, 129/132.
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 678/24,129/132?
Given fractions are 678/24,129/132
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 678/24,129/132, numerators are 678,129
Denominators are 24,132
The GCF of 678,129 is 3 .
LCM of 24,132 is 264.
The greatest common factor of 678/24,129/132 = [GCF of 678,129]/[LCM of 24,132]= 3/264
Therefore, the GCF of 678/24,129/132 is 3/264.
To find the highest common factor of 678,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 129 are 1, 3, 43, 129
The HCF of 678,129 is 3.
Lets's calculate GCF of 678,129
| 3 | 678, 129 |
| 226, 43 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 678,129 By Matching Biggest Common Factor Method
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 678,129 . The biggest common factor number is the GCF number.
So the greatest common factor 678,129 is 3.
Lets's calculate LCM of 24,132
| 2 | 24, 132 |
| 2 | 12, 66 |
| 3 | 6, 33 |
| 2, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 11 = 264
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/264
Therefore, the GCF of Fractions 678/24,129/132 is 3/264
Least Common Multiple of 24,132 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 24,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,132) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(24,132) x common factors =12 x 1 = 12
LCM(24,132) = ( 24 × 132 ) / 12
LCM(24,132) = 3168 / 12
LCM(24,132) = 264
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FAQs on GCF of Fractions of 678/24, 129/132
1. What is the HCF of 678,129?
The HCF of 678,129 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 678/24, 129/132?
Answer: GCF of Numerators as per given numbers 678/24, 129/132 is
GCF of Numerators i.e. for 678,129 is 3
LCM of denominators i.e. for 24,132 is 264.
Thus, GCF of Fractions is 3/264.Finally, GCF of Fractions for 678/24, 129/132 is 3/264.