GCF of 39/105, 69/7749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 39/105, 69/7749 i.e 3/38745 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/105, 69/7749.
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 39/105,69/7749?
Given fractions are 39/105,69/7749
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 39/105,69/7749, numerators are 39,69
Denominators are 105,7749
The GCF of 39,69 is 3 .
LCM of 105,7749 is 38745.
The greatest common factor of 39/105,69/7749 = [GCF of 39,69]/[LCM of 105,7749]= 3/38745
Therefore, the GCF of 39/105,69/7749 is 3/38745.
To find the highest common factor of 39,69, 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 69 are 1, 3, 23, 69
The HCF of 39,69 is 3.
Lets's calculate GCF of 39,69
| 3 | 39, 69 |
| 13, 23 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 39,69 By Matching Biggest Common Factor Method
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 69
:1,3,23,69
Greatest Common Factor
We found the factors 39,69 . The biggest common factor number is the GCF number.
So the greatest common factor 39,69 is 3.
Lets's calculate LCM of 105,7749
| 3 | 105, 7749 |
| 7 | 35, 2583 |
| 5, 369 |
∴ So the LCM of the given numbers is 3 x 7 x 5 x 369 = 38745
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/38745
Therefore, the GCF of Fractions 39/105,69/7749 is 3/38745
Least Common Multiple of 105,7749 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 105,7749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,7749) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(105,7749) x common factors =21 x 1 = 21
LCM(105,7749) = ( 105 × 7749 ) / 21
LCM(105,7749) = 813645 / 21
LCM(105,7749) = 38745
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FAQs on GCF of Fractions of 39/105, 69/7749
1. What is the HCF of 39,69?
The HCF of 39,69 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 39/105, 69/7749?
Answer: GCF of Numerators as per given numbers 39/105, 69/7749 is
GCF of Numerators i.e. for 39,69 is 3
LCM of denominators i.e. for 105,7749 is 38745.
Thus, GCF of Fractions is 3/38745.Finally, GCF of Fractions for 39/105, 69/7749 is 3/38745.