GCF of 39/54, 42/60, 39/72
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 39/54, 42/60, 39/72 i.e 3/1080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/54, 42/60, 39/72.
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 39/54,42/60,39/72?
Given fractions are 39/54,42/60,39/72
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 39/54,42/60,39/72, numerators are 39,42,39
Denominators are 54,60,72
The GCF of 39,42,39 is 3 .
LCM of 54,60,72 is 1080.
The greatest common factor of 39/54,42/60,39/72 = [GCF of 39,42,39]/[LCM of 54,60,72]= 3/1080
Therefore, the GCF of 39/54,42/60,39/72 is 3/1080.
To find the highest common factor of 39,42,39, we have to find the factors of both numbers and list the highest common factor.
The factors of 39 are 1, 3, 13, 39
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 39 are 1, 3, 13, 39
The HCF of 39,42,39 is 3.
Lets's calculate GCF of 39,42,39
| 3 | 39, 42, 39 |
| 13, 14, 13 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 39,42,39 By Matching Biggest Common Factor Method
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 39
:1,3,13,39
Greatest Common Factor
We found the factors 39,42,39 . The biggest common factor number is the GCF number.
So the greatest common factor 39,42,39 is 3.
Lets's calculate LCM of 54,60,72
| 2 | 54, 60, 72 |
| 2 | 27, 30, 36 |
| 3 | 27, 15, 18 |
| 3 | 9, 5, 6 |
| 3, 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 5 x 2 = 1080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1080
Therefore, the GCF of Fractions 39/54,42/60,39/72 is 3/1080
Least Common Multiple of 54,60,72 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 54,60,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,60,72) = 6
common factors(in case of two or more numbers have common factors) = 36
GCF(54,60,72) x common factors =6 x 36 = 216
LCM(54,60,72) = ( 54 × 60 × 72 ) / 216
LCM(54,60,72) = 233280 / 216
LCM(54,60,72) = 1080
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FAQs on GCF of Fractions of 39/54, 42/60, 39/72
1. What is the HCF of 39,42,39?
The HCF of 39,42,39 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 39/54, 42/60, 39/72?
Answer: GCF of Numerators as per given numbers 39/54, 42/60, 39/72 is
GCF of Numerators i.e. for 39,42,39 is 3
LCM of denominators i.e. for 54,60,72 is 1080.
Thus, GCF of Fractions is 3/1080.Finally, GCF of Fractions for 39/54, 42/60, 39/72 is 3/1080.