GCF of 23/60, 65/23, 15/23, 42/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 23/60, 65/23, 15/23, 42/21 i.e 1/9660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/60, 65/23, 15/23, 42/21.
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 23/60,65/23,15/23,42/21?
Given fractions are 23/60,65/23,15/23,42/21
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 23/60,65/23,15/23,42/21, numerators are 23,65,15,42
Denominators are 60,23,23,21
The GCF of 23,65,15,42 is 1 .
LCM of 60,23,23,21 is 9660.
The greatest common factor of 23/60,65/23,15/23,42/21 = [GCF of 23,65,15,42]/[LCM of 60,23,23,21]= 1/9660
Therefore, the GCF of 23/60,65/23,15/23,42/21 is 1/9660.
To find the highest common factor of 23,65,15,42, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 65 are 1, 5, 13, 65
The factors of 15 are 1, 3, 5, 15
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The HCF of 23,65,15,42 is 1.
Lets's calculate GCF of 23,65,15,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 23,65,15,42 By Matching Biggest Common Factor Method
Now, list down the factors of 23
:1,23
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 23,65,15,42 . The biggest common factor number is the GCF number.
So the greatest common factor 23,65,15,42 is 1.
Lets's calculate LCM of 60,23,23,21
| 3 | 60, 23, 23, 21 |
| 23 | 20, 23, 23, 7 |
| 20, 1, 1, 7 |
∴ So the LCM of the given numbers is 3 x 23 x 20 x 1 x 1 x 7 = 9660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9660
Therefore, the GCF of Fractions 23/60,65/23,15/23,42/21 is 1/9660
Least Common Multiple of 60,23,23,21 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 60,23,23,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,23,23,21) = 1
common factors(in case of two or more numbers have common factors) = 69
GCF(60,23,23,21) x common factors =1 x 69 = 69
LCM(60,23,23,21) = ( 60 × 23 × 23 × 21 ) / 69
LCM(60,23,23,21) = 666540 / 69
LCM(60,23,23,21) = 9660
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FAQs on GCF of Fractions of 23/60, 65/23, 15/23, 42/21
1. What is the HCF of 23,65,15,42?
The HCF of 23,65,15,42 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 23/60, 65/23, 15/23, 42/21?
Answer: GCF of Numerators as per given numbers 23/60, 65/23, 15/23, 42/21 is
GCF of Numerators i.e. for 23,65,15,42 is 1
LCM of denominators i.e. for 60,23,23,21 is 9660.
Thus, GCF of Fractions is 1/9660.Finally, GCF of Fractions for 23/60, 65/23, 15/23, 42/21 is 1/9660.