GCF of 369/456, 768/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 369/456, 768/174 i.e 3/13224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 369/456, 768/174.
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 369/456,768/174?
Given fractions are 369/456,768/174
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 369/456,768/174, numerators are 369,768
Denominators are 456,174
The GCF of 369,768 is 3 .
LCM of 456,174 is 13224.
The greatest common factor of 369/456,768/174 = [GCF of 369,768]/[LCM of 456,174]= 3/13224
Therefore, the GCF of 369/456,768/174 is 3/13224.
To find the highest common factor of 369,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 369 are 1, 3, 9, 41, 123, 369
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 369,768 is 3.
Lets's calculate GCF of 369,768
| 3 | 369, 768 |
| 123, 256 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 369,768 By Matching Biggest Common Factor Method
Now, list down the factors of 369
:1,3,9,41,123,369
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 369,768 . The biggest common factor number is the GCF number.
So the greatest common factor 369,768 is 3.
Lets's calculate LCM of 456,174
| 2 | 456, 174 |
| 3 | 228, 87 |
| 76, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 76 x 29 = 13224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13224
Therefore, the GCF of Fractions 369/456,768/174 is 3/13224
Least Common Multiple of 456,174 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 456,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(456,174) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(456,174) x common factors =6 x 1 = 6
LCM(456,174) = ( 456 × 174 ) / 6
LCM(456,174) = 79344 / 6
LCM(456,174) = 13224
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FAQs on GCF of Fractions of 369/456, 768/174
1. What is the HCF of 369,768?
The HCF of 369,768 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 369/456, 768/174?
Answer: GCF of Numerators as per given numbers 369/456, 768/174 is
GCF of Numerators i.e. for 369,768 is 3
LCM of denominators i.e. for 456,174 is 13224.
Thus, GCF of Fractions is 3/13224.Finally, GCF of Fractions for 369/456, 768/174 is 3/13224.