GCF of 29/15, 42/81, 32/270
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 29/15, 42/81, 32/270 i.e 1/810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/15, 42/81, 32/270.
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 29/15,42/81,32/270?
Given fractions are 29/15,42/81,32/270
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 29/15,42/81,32/270, numerators are 29,42,32
Denominators are 15,81,270
The GCF of 29,42,32 is 1 .
LCM of 15,81,270 is 810.
The greatest common factor of 29/15,42/81,32/270 = [GCF of 29,42,32]/[LCM of 15,81,270]= 1/810
Therefore, the GCF of 29/15,42/81,32/270 is 1/810.
To find the highest common factor of 29,42,32, we have to find the factors of both numbers and list the highest common factor.
The factors of 29 are 1, 29
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 32 are 1, 2, 4, 8, 16, 32
The HCF of 29,42,32 is 1.
Lets's calculate GCF of 29,42,32
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 29,42,32 By Matching Biggest Common Factor Method
Now, list down the factors of 29
:1,29
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 32
:1,2,4,8,16,32
Greatest Common Factor
We found the factors 29,42,32 . The biggest common factor number is the GCF number.
So the greatest common factor 29,42,32 is 1.
Lets's calculate LCM of 15,81,270
| 3 | 15, 81, 270 |
| 3 | 5, 27, 90 |
| 3 | 5, 9, 30 |
| 5 | 5, 3, 10 |
| 1, 3, 2 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 5 x 1 x 3 x 2 = 810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/810
Therefore, the GCF of Fractions 29/15,42/81,32/270 is 1/810
Least Common Multiple of 15,81,270 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 15,81,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,81,270) = 3
common factors(in case of two or more numbers have common factors) = 135
GCF(15,81,270) x common factors =3 x 135 = 405
LCM(15,81,270) = ( 15 × 81 × 270 ) / 405
LCM(15,81,270) = 328050 / 405
LCM(15,81,270) = 810
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FAQs on GCF of Fractions of 29/15, 42/81, 32/270
1. What is the HCF of 29,42,32?
The HCF of 29,42,32 is 1
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 29/15, 42/81, 32/270?
Answer: GCF of Numerators as per given numbers 29/15, 42/81, 32/270 is
GCF of Numerators i.e. for 29,42,32 is 1
LCM of denominators i.e. for 15,81,270 is 810.
Thus, GCF of Fractions is 1/810.Finally, GCF of Fractions for 29/15, 42/81, 32/270 is 1/810.