GCF of 11/75, 42/69, 65/76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 11/75, 42/69, 65/76 i.e 1/131100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 11/75, 42/69, 65/76.
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 11/75,42/69,65/76?
Given fractions are 11/75,42/69,65/76
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 11/75,42/69,65/76, numerators are 11,42,65
Denominators are 75,69,76
The GCF of 11,42,65 is 1 .
LCM of 75,69,76 is 131100.
The greatest common factor of 11/75,42/69,65/76 = [GCF of 11,42,65]/[LCM of 75,69,76]= 1/131100
Therefore, the GCF of 11/75,42/69,65/76 is 1/131100.
To find the highest common factor of 11,42,65, we have to find the factors of both numbers and list the highest common factor.
The factors of 11 are 1, 11
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 65 are 1, 5, 13, 65
The HCF of 11,42,65 is 1.
Lets's calculate GCF of 11,42,65
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 11,42,65 By Matching Biggest Common Factor Method
Now, list down the factors of 11
:1,11
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 65
:1,5,13,65
Greatest Common Factor
We found the factors 11,42,65 . The biggest common factor number is the GCF number.
So the greatest common factor 11,42,65 is 1.
Lets's calculate LCM of 75,69,76
| 3 | 75, 69, 76 |
| 25, 23, 76 |
∴ So the LCM of the given numbers is 3 x 25 x 23 x 76 = 131100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/131100
Therefore, the GCF of Fractions 11/75,42/69,65/76 is 1/131100
Least Common Multiple of 75,69,76 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 75,69,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,69,76) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(75,69,76) x common factors =1 x 3 = 3
LCM(75,69,76) = ( 75 × 69 × 76 ) / 3
LCM(75,69,76) = 393300 / 3
LCM(75,69,76) = 131100
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FAQs on GCF of Fractions of 11/75, 42/69, 65/76
1. What is the HCF of 11,42,65?
The HCF of 11,42,65 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 11/75, 42/69, 65/76?
Answer: GCF of Numerators as per given numbers 11/75, 42/69, 65/76 is
GCF of Numerators i.e. for 11,42,65 is 1
LCM of denominators i.e. for 75,69,76 is 131100.
Thus, GCF of Fractions is 1/131100.Finally, GCF of Fractions for 11/75, 42/69, 65/76 is 1/131100.