GCF of 73/23, 14/46, 88/21, 13/30
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 73/23, 14/46, 88/21, 13/30 i.e 1/4830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 73/23, 14/46, 88/21, 13/30.
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 73/23,14/46,88/21,13/30?
Given fractions are 73/23,14/46,88/21,13/30
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 73/23,14/46,88/21,13/30, numerators are 73,14,88,13
Denominators are 23,46,21,30
The GCF of 73,14,88,13 is 1 .
LCM of 23,46,21,30 is 4830.
The greatest common factor of 73/23,14/46,88/21,13/30 = [GCF of 73,14,88,13]/[LCM of 23,46,21,30]= 1/4830
Therefore, the GCF of 73/23,14/46,88/21,13/30 is 1/4830.
To find the highest common factor of 73,14,88,13, we have to find the factors of both numbers and list the highest common factor.
The factors of 73 are 1, 73
The factors of 14 are 1, 2, 7, 14
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88
The factors of 13 are 1, 13
The HCF of 73,14,88,13 is 1.
Lets's calculate GCF of 73,14,88,13
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 73,14,88,13 By Matching Biggest Common Factor Method
Now, list down the factors of 73
:1,73
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 88
:1,2,4,8,11,22,44,88
Now, list down the factors of 13
:1,13
Greatest Common Factor
We found the factors 73,14,88,13 . The biggest common factor number is the GCF number.
So the greatest common factor 73,14,88,13 is 1.
Lets's calculate LCM of 23,46,21,30
| 2 | 23, 46, 21, 30 |
| 3 | 23, 23, 21, 15 |
| 23 | 23, 23, 7, 5 |
| 1, 1, 7, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 1 x 1 x 7 x 5 = 4830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4830
Therefore, the GCF of Fractions 73/23,14/46,88/21,13/30 is 1/4830
Least Common Multiple of 23,46,21,30 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 23,46,21,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,46,21,30) = 1
common factors(in case of two or more numbers have common factors) = 138
GCF(23,46,21,30) x common factors =1 x 138 = 138
LCM(23,46,21,30) = ( 23 × 46 × 21 × 30 ) / 138
LCM(23,46,21,30) = 666540 / 138
LCM(23,46,21,30) = 4830
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 73/23, 14/46, 88/21, 13/30
1. What is the HCF of 73,14,88,13?
The HCF of 73,14,88,13 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 73/23, 14/46, 88/21, 13/30?
Answer: GCF of Numerators as per given numbers 73/23, 14/46, 88/21, 13/30 is
GCF of Numerators i.e. for 73,14,88,13 is 1
LCM of denominators i.e. for 23,46,21,30 is 4830.
Thus, GCF of Fractions is 1/4830.Finally, GCF of Fractions for 73/23, 14/46, 88/21, 13/30 is 1/4830.