GCF of 65/90, 578/21, 378/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 65/90, 578/21, 378/686 i.e 1/30870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/90, 578/21, 378/686.
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 65/90,578/21,378/686?
Given fractions are 65/90,578/21,378/686
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 65/90,578/21,378/686, numerators are 65,578,378
Denominators are 90,21,686
The GCF of 65,578,378 is 1 .
LCM of 90,21,686 is 30870.
The greatest common factor of 65/90,578/21,378/686 = [GCF of 65,578,378]/[LCM of 90,21,686]= 1/30870
Therefore, the GCF of 65/90,578/21,378/686 is 1/30870.
To find the highest common factor of 65,578,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 65,578,378 is 1.
Lets's calculate GCF of 65,578,378
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 65,578,378 By Matching Biggest Common Factor Method
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 65,578,378 . The biggest common factor number is the GCF number.
So the greatest common factor 65,578,378 is 1.
Lets's calculate LCM of 90,21,686
| 2 | 90, 21, 686 |
| 3 | 45, 21, 343 |
| 7 | 15, 7, 343 |
| 15, 1, 49 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 15 x 1 x 49 = 30870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30870
Therefore, the GCF of Fractions 65/90,578/21,378/686 is 1/30870
Least Common Multiple of 90,21,686 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 90,21,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,21,686) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(90,21,686) x common factors =1 x 42 = 42
LCM(90,21,686) = ( 90 × 21 × 686 ) / 42
LCM(90,21,686) = 1296540 / 42
LCM(90,21,686) = 30870
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FAQs on GCF of Fractions of 65/90, 578/21, 378/686
1. What is the HCF of 65,578,378?
The HCF of 65,578,378 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 65/90, 578/21, 378/686?
Answer: GCF of Numerators as per given numbers 65/90, 578/21, 378/686 is
GCF of Numerators i.e. for 65,578,378 is 1
LCM of denominators i.e. for 90,21,686 is 30870.
Thus, GCF of Fractions is 1/30870.Finally, GCF of Fractions for 65/90, 578/21, 378/686 is 1/30870.