GCF of 65/21, 63/54, 66/69, 78/23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 65/21, 63/54, 66/69, 78/23 i.e 1/8694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/21, 63/54, 66/69, 78/23.
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 65/21,63/54,66/69,78/23?
Given fractions are 65/21,63/54,66/69,78/23
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 65/21,63/54,66/69,78/23, numerators are 65,63,66,78
Denominators are 21,54,69,23
The GCF of 65,63,66,78 is 1 .
LCM of 21,54,69,23 is 8694.
The greatest common factor of 65/21,63/54,66/69,78/23 = [GCF of 65,63,66,78]/[LCM of 21,54,69,23]= 1/8694
Therefore, the GCF of 65/21,63/54,66/69,78/23 is 1/8694.
To find the highest common factor of 65,63,66,78, 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 63 are 1, 3, 7, 9, 21, 63
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The HCF of 65,63,66,78 is 1.
Lets's calculate GCF of 65,63,66,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 65,63,66,78 By Matching Biggest Common Factor Method
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 65,63,66,78 . The biggest common factor number is the GCF number.
So the greatest common factor 65,63,66,78 is 1.
Lets's calculate LCM of 21,54,69,23
| 3 | 21, 54, 69, 23 |
| 23 | 7, 18, 23, 23 |
| 7, 18, 1, 1 |
∴ So the LCM of the given numbers is 3 x 23 x 7 x 18 x 1 x 1 = 8694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8694
Therefore, the GCF of Fractions 65/21,63/54,66/69,78/23 is 1/8694
Least Common Multiple of 21,54,69,23 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 21,54,69,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,54,69,23) = 1
common factors(in case of two or more numbers have common factors) = 207
GCF(21,54,69,23) x common factors =1 x 207 = 207
LCM(21,54,69,23) = ( 21 × 54 × 69 × 23 ) / 207
LCM(21,54,69,23) = 1799658 / 207
LCM(21,54,69,23) = 8694
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 65/21, 63/54, 66/69, 78/23
1. What is the HCF of 65,63,66,78?
The HCF of 65,63,66,78 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 65/21, 63/54, 66/69, 78/23?
Answer: GCF of Numerators as per given numbers 65/21, 63/54, 66/69, 78/23 is
GCF of Numerators i.e. for 65,63,66,78 is 1
LCM of denominators i.e. for 21,54,69,23 is 8694.
Thus, GCF of Fractions is 1/8694.Finally, GCF of Fractions for 65/21, 63/54, 66/69, 78/23 is 1/8694.