GCF of 119/512, 756/666
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 119/512, 756/666 i.e 7/170496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 119/512, 756/666.
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 119/512,756/666?
Given fractions are 119/512,756/666
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 119/512,756/666, numerators are 119,756
Denominators are 512,666
The GCF of 119,756 is 7 .
LCM of 512,666 is 170496.
The greatest common factor of 119/512,756/666 = [GCF of 119,756]/[LCM of 512,666]= 7/170496
Therefore, the GCF of 119/512,756/666 is 7/170496.
To find the highest common factor of 119,756, we have to find the factors of both numbers and list the highest common factor.
The factors of 119 are 1, 7, 17, 119
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 HCF of 119,756 is 7.
Lets's calculate GCF of 119,756
| 7 | 119, 756 |
| 17, 108 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 119,756 By Matching Biggest Common Factor Method
Now, list down the factors of 119
:1,7,17,119
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
Greatest Common Factor
We found the factors 119,756 . The biggest common factor number is the GCF number.
So the greatest common factor 119,756 is 7.
Lets's calculate LCM of 512,666
| 2 | 512, 666 |
| 256, 333 |
∴ So the LCM of the given numbers is 2 x 256 x 333 = 170496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/170496
Therefore, the GCF of Fractions 119/512,756/666 is 7/170496
Least Common Multiple of 512,666 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 512,666 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,666) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,666) x common factors =2 x 1 = 2
LCM(512,666) = ( 512 × 666 ) / 2
LCM(512,666) = 340992 / 2
LCM(512,666) = 170496
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FAQs on GCF of Fractions of 119/512, 756/666
1. What is the HCF of 119,756?
The HCF of 119,756 is 7
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 119/512, 756/666?
Answer: GCF of Numerators as per given numbers 119/512, 756/666 is
GCF of Numerators i.e. for 119,756 is 7
LCM of denominators i.e. for 512,666 is 170496.
Thus, GCF of Fractions is 7/170496.Finally, GCF of Fractions for 119/512, 756/666 is 7/170496.