GCF of 132/756, 912/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 132/756, 912/814 i.e 12/307692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/756, 912/814.
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 132/756,912/814?
Given fractions are 132/756,912/814
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 132/756,912/814, numerators are 132,912
Denominators are 756,814
The GCF of 132,912 is 12 .
LCM of 756,814 is 307692.
The greatest common factor of 132/756,912/814 = [GCF of 132,912]/[LCM of 756,814]= 12/307692
Therefore, the GCF of 132/756,912/814 is 12/307692.
To find the highest common factor of 132,912, we have to find the factors of both numbers and list the highest common factor.
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The factors of 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912
The HCF of 132,912 is 12.
Lets's calculate GCF of 132,912
| 2 | 132, 912 |
| 2 | 66, 456 |
| 3 | 33, 228 |
| 11, 76 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 132,912 By Matching Biggest Common Factor Method
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Now, list down the factors of 912
:1,2,3,4,6,8,12,16,19,24,38,48,57,76,114,152,228,304,456,912
Greatest Common Factor
We found the factors 132,912 . The biggest common factor number is the GCF number.
So the greatest common factor 132,912 is 12.
Lets's calculate LCM of 756,814
| 2 | 756, 814 |
| 378, 407 |
∴ So the LCM of the given numbers is 2 x 378 x 407 = 307692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/307692
Therefore, the GCF of Fractions 132/756,912/814 is 12/307692
Least Common Multiple of 756,814 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 756,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(756,814) x common factors =2 x 1 = 2
LCM(756,814) = ( 756 × 814 ) / 2
LCM(756,814) = 615384 / 2
LCM(756,814) = 307692
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FAQs on GCF of Fractions of 132/756, 912/814
1. What is the HCF of 132,912?
The HCF of 132,912 is 12
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 132/756, 912/814?
Answer: GCF of Numerators as per given numbers 132/756, 912/814 is
GCF of Numerators i.e. for 132,912 is 12
LCM of denominators i.e. for 756,814 is 307692.
Thus, GCF of Fractions is 12/307692.Finally, GCF of Fractions for 132/756, 912/814 is 12/307692.