GCF of 756/164, 378/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 756/164, 378/129 i.e 378/21156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/164, 378/129.
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 756/164,378/129?
Given fractions are 756/164,378/129
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 756/164,378/129, numerators are 756,378
Denominators are 164,129
The GCF of 756,378 is 378 .
LCM of 164,129 is 21156.
The greatest common factor of 756/164,378/129 = [GCF of 756,378]/[LCM of 164,129]= 378/21156
Therefore, the GCF of 756/164,378/129 is 378/21156.
To find the highest common factor of 756,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 756,378 is 378.
Lets's calculate GCF of 756,378
| 2 | 756, 378 |
| 3 | 378, 189 |
| 3 | 126, 63 |
| 3 | 42, 21 |
| 7 | 14, 7 |
| 2, 1 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 x 7 = 378
Greatest Common Factor of 756,378 By Matching Biggest Common Factor Method
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 756,378 . The biggest common factor number is the GCF number.
So the greatest common factor 756,378 is 378.
Lets's calculate LCM of 164,129
Given numbers has no common factors except 1. So, there LCM is their product i.e 21156
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 378/21156
Therefore, the GCF of Fractions 756/164,378/129 is 378/21156
Least Common Multiple of 164,129 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 164,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(164,129) x common factors =1 x 1 = 1
LCM(164,129) = ( 164 × 129 ) / 1
LCM(164,129) = 21156 / 1
LCM(164,129) = 21156
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FAQs on GCF of Fractions of 756/164, 378/129
1. What is the HCF of 756,378?
The HCF of 756,378 is 378
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 756/164, 378/129?
Answer: GCF of Numerators as per given numbers 756/164, 378/129 is
GCF of Numerators i.e. for 756,378 is 378
LCM of denominators i.e. for 164,129 is 21156.
Thus, GCF of Fractions is 378/21156.Finally, GCF of Fractions for 756/164, 378/129 is 378/21156.