GCF of 26/21, 98/78, 69/975
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 26/21, 98/78, 69/975 i.e 1/13650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 26/21, 98/78, 69/975.
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 26/21,98/78,69/975?
Given fractions are 26/21,98/78,69/975
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 26/21,98/78,69/975, numerators are 26,98,69
Denominators are 21,78,975
The GCF of 26,98,69 is 1 .
LCM of 21,78,975 is 13650.
The greatest common factor of 26/21,98/78,69/975 = [GCF of 26,98,69]/[LCM of 21,78,975]= 1/13650
Therefore, the GCF of 26/21,98/78,69/975 is 1/13650.
To find the highest common factor of 26,98,69, we have to find the factors of both numbers and list the highest common factor.
The factors of 26 are 1, 2, 13, 26
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 69 are 1, 3, 23, 69
The HCF of 26,98,69 is 1.
Lets's calculate GCF of 26,98,69
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 26,98,69 By Matching Biggest Common Factor Method
Now, list down the factors of 26
:1,2,13,26
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 69
:1,3,23,69
Greatest Common Factor
We found the factors 26,98,69 . The biggest common factor number is the GCF number.
So the greatest common factor 26,98,69 is 1.
Lets's calculate LCM of 21,78,975
| 3 | 21, 78, 975 |
| 13 | 7, 26, 325 |
| 7, 2, 25 |
∴ So the LCM of the given numbers is 3 x 13 x 7 x 2 x 25 = 13650
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13650
Therefore, the GCF of Fractions 26/21,98/78,69/975 is 1/13650
Least Common Multiple of 21,78,975 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 21,78,975 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,78,975) = 3
common factors(in case of two or more numbers have common factors) = 39
GCF(21,78,975) x common factors =3 x 39 = 117
LCM(21,78,975) = ( 21 × 78 × 975 ) / 117
LCM(21,78,975) = 1597050 / 117
LCM(21,78,975) = 13650
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FAQs on GCF of Fractions of 26/21, 98/78, 69/975
1. What is the HCF of 26,98,69?
The HCF of 26,98,69 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 26/21, 98/78, 69/975?
Answer: GCF of Numerators as per given numbers 26/21, 98/78, 69/975 is
GCF of Numerators i.e. for 26,98,69 is 1
LCM of denominators i.e. for 21,78,975 is 13650.
Thus, GCF of Fractions is 1/13650.Finally, GCF of Fractions for 26/21, 98/78, 69/975 is 1/13650.