GCF of 132/78, 315/577
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 132/78, 315/577 i.e 3/45006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/78, 315/577.
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 132/78,315/577?
Given fractions are 132/78,315/577
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 132/78,315/577, numerators are 132,315
Denominators are 78,577
The GCF of 132,315 is 3 .
LCM of 78,577 is 45006.
The greatest common factor of 132/78,315/577 = [GCF of 132,315]/[LCM of 78,577]= 3/45006
Therefore, the GCF of 132/78,315/577 is 3/45006.
To find the highest common factor of 132,315, 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 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The HCF of 132,315 is 3.
Lets's calculate GCF of 132,315
| 3 | 132, 315 |
| 44, 105 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 132,315 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 315
:1,3,5,7,9,15,21,35,45,63,105,315
Greatest Common Factor
We found the factors 132,315 . The biggest common factor number is the GCF number.
So the greatest common factor 132,315 is 3.
Lets's calculate LCM of 78,577
Given numbers has no common factors except 1. So, there LCM is their product i.e 45006
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/45006
Therefore, the GCF of Fractions 132/78,315/577 is 3/45006
Least Common Multiple of 78,577 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 78,577 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,577) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(78,577) x common factors =1 x 1 = 1
LCM(78,577) = ( 78 × 577 ) / 1
LCM(78,577) = 45006 / 1
LCM(78,577) = 45006
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FAQs on GCF of Fractions of 132/78, 315/577
1. What is the HCF of 132,315?
The HCF of 132,315 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 132/78, 315/577?
Answer: GCF of Numerators as per given numbers 132/78, 315/577 is
GCF of Numerators i.e. for 132,315 is 3
LCM of denominators i.e. for 78,577 is 45006.
Thus, GCF of Fractions is 3/45006.Finally, GCF of Fractions for 132/78, 315/577 is 3/45006.