GCF of 13/14, 59/21, 70/45, 23/197
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 13/14, 59/21, 70/45, 23/197 i.e 1/124110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/14, 59/21, 70/45, 23/197.
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 13/14,59/21,70/45,23/197?
Given fractions are 13/14,59/21,70/45,23/197
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 13/14,59/21,70/45,23/197, numerators are 13,59,70,23
Denominators are 14,21,45,197
The GCF of 13,59,70,23 is 1 .
LCM of 14,21,45,197 is 124110.
The greatest common factor of 13/14,59/21,70/45,23/197 = [GCF of 13,59,70,23]/[LCM of 14,21,45,197]= 1/124110
Therefore, the GCF of 13/14,59/21,70/45,23/197 is 1/124110.
To find the highest common factor of 13,59,70,23, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 59 are 1, 59
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 23 are 1, 23
The HCF of 13,59,70,23 is 1.
Lets's calculate GCF of 13,59,70,23
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 13,59,70,23 By Matching Biggest Common Factor Method
Now, list down the factors of 13
:1,13
Now, list down the factors of 59
:1,59
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 23
:1,23
Greatest Common Factor
We found the factors 13,59,70,23 . The biggest common factor number is the GCF number.
So the greatest common factor 13,59,70,23 is 1.
Lets's calculate LCM of 14,21,45,197
| 3 | 14, 21, 45, 197 |
| 7 | 14, 7, 15, 197 |
| 2, 1, 15, 197 |
∴ So the LCM of the given numbers is 3 x 7 x 2 x 1 x 15 x 197 = 124110
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/124110
Therefore, the GCF of Fractions 13/14,59/21,70/45,23/197 is 1/124110
Least Common Multiple of 14,21,45,197 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 14,21,45,197 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,21,45,197) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(14,21,45,197) x common factors =1 x 21 = 21
LCM(14,21,45,197) = ( 14 × 21 × 45 × 197 ) / 21
LCM(14,21,45,197) = 2606310 / 21
LCM(14,21,45,197) = 124110
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 13/14, 59/21, 70/45, 23/197
1. What is the HCF of 13,59,70,23?
The HCF of 13,59,70,23 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 13/14, 59/21, 70/45, 23/197?
Answer: GCF of Numerators as per given numbers 13/14, 59/21, 70/45, 23/197 is
GCF of Numerators i.e. for 13,59,70,23 is 1
LCM of denominators i.e. for 14,21,45,197 is 124110.
Thus, GCF of Fractions is 1/124110.Finally, GCF of Fractions for 13/14, 59/21, 70/45, 23/197 is 1/124110.