GCF of 132/32, 312/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 132/32, 312/978 i.e 12/15648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/32, 312/978.
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 132/32,312/978?
Given fractions are 132/32,312/978
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 132/32,312/978, numerators are 132,312
Denominators are 32,978
The GCF of 132,312 is 12 .
LCM of 32,978 is 15648.
The greatest common factor of 132/32,312/978 = [GCF of 132,312]/[LCM of 32,978]= 12/15648
Therefore, the GCF of 132/32,312/978 is 12/15648.
To find the highest common factor of 132,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 132,312 is 12.
Lets's calculate GCF of 132,312
| 2 | 132, 312 |
| 2 | 66, 156 |
| 3 | 33, 78 |
| 11, 26 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 132,312 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 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 132,312 . The biggest common factor number is the GCF number.
So the greatest common factor 132,312 is 12.
Lets's calculate LCM of 32,978
| 2 | 32, 978 |
| 16, 489 |
∴ So the LCM of the given numbers is 2 x 16 x 489 = 15648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/15648
Therefore, the GCF of Fractions 132/32,312/978 is 12/15648
Least Common Multiple of 32,978 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 32,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,978) x common factors =2 x 1 = 2
LCM(32,978) = ( 32 × 978 ) / 2
LCM(32,978) = 31296 / 2
LCM(32,978) = 15648
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FAQs on GCF of Fractions of 132/32, 312/978
1. What is the HCF of 132,312?
The HCF of 132,312 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 132/32, 312/978?
Answer: GCF of Numerators as per given numbers 132/32, 312/978 is
GCF of Numerators i.e. for 132,312 is 12
LCM of denominators i.e. for 32,978 is 15648.
Thus, GCF of Fractions is 12/15648.Finally, GCF of Fractions for 132/32, 312/978 is 12/15648.