GCF of 345/36, 713/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 345/36, 713/132 i.e 23/396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 345/36, 713/132.
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 345/36,713/132?
Given fractions are 345/36,713/132
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 345/36,713/132, numerators are 345,713
Denominators are 36,132
The GCF of 345,713 is 23 .
LCM of 36,132 is 396.
The greatest common factor of 345/36,713/132 = [GCF of 345,713]/[LCM of 36,132]= 23/396
Therefore, the GCF of 345/36,713/132 is 23/396.
To find the highest common factor of 345,713, we have to find the factors of both numbers and list the highest common factor.
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The factors of 713 are 1, 23, 31, 713
The HCF of 345,713 is 23.
Lets's calculate GCF of 345,713
| 23 | 345, 713 |
| 15, 31 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 345,713 By Matching Biggest Common Factor Method
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Now, list down the factors of 713
:1,23,31,713
Greatest Common Factor
We found the factors 345,713 . The biggest common factor number is the GCF number.
So the greatest common factor 345,713 is 23.
Lets's calculate LCM of 36,132
| 2 | 36, 132 |
| 2 | 18, 66 |
| 3 | 9, 33 |
| 3, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 11 = 396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/396
Therefore, the GCF of Fractions 345/36,713/132 is 23/396
Least Common Multiple of 36,132 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 36,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,132) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(36,132) x common factors =12 x 1 = 12
LCM(36,132) = ( 36 × 132 ) / 12
LCM(36,132) = 4752 / 12
LCM(36,132) = 396
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FAQs on GCF of Fractions of 345/36, 713/132
1. What is the HCF of 345,713?
The HCF of 345,713 is 23
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 345/36, 713/132?
Answer: GCF of Numerators as per given numbers 345/36, 713/132 is
GCF of Numerators i.e. for 345,713 is 23
LCM of denominators i.e. for 36,132 is 396.
Thus, GCF of Fractions is 23/396.Finally, GCF of Fractions for 345/36, 713/132 is 23/396.