GCF of 34/25, 45/16, 588/968
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/25, 45/16, 588/968 i.e 1/48400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/25, 45/16, 588/968.
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 34/25,45/16,588/968?
Given fractions are 34/25,45/16,588/968
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 34/25,45/16,588/968, numerators are 34,45,588
Denominators are 25,16,968
The GCF of 34,45,588 is 1 .
LCM of 25,16,968 is 48400.
The greatest common factor of 34/25,45/16,588/968 = [GCF of 34,45,588]/[LCM of 25,16,968]= 1/48400
Therefore, the GCF of 34/25,45/16,588/968 is 1/48400.
To find the highest common factor of 34,45,588, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The HCF of 34,45,588 is 1.
Lets's calculate GCF of 34,45,588
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,45,588 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 588
:1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588
Greatest Common Factor
We found the factors 34,45,588 . The biggest common factor number is the GCF number.
So the greatest common factor 34,45,588 is 1.
Lets's calculate LCM of 25,16,968
| 2 | 25, 16, 968 |
| 2 | 25, 8, 484 |
| 2 | 25, 4, 242 |
| 25, 2, 121 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 25 x 2 x 121 = 48400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/48400
Therefore, the GCF of Fractions 34/25,45/16,588/968 is 1/48400
Least Common Multiple of 25,16,968 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 25,16,968 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,16,968) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(25,16,968) x common factors =1 x 8 = 8
LCM(25,16,968) = ( 25 × 16 × 968 ) / 8
LCM(25,16,968) = 387200 / 8
LCM(25,16,968) = 48400
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 34/25, 45/16, 588/968
1. What is the HCF of 34,45,588?
The HCF of 34,45,588 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 34/25, 45/16, 588/968?
Answer: GCF of Numerators as per given numbers 34/25, 45/16, 588/968 is
GCF of Numerators i.e. for 34,45,588 is 1
LCM of denominators i.e. for 25,16,968 is 48400.
Thus, GCF of Fractions is 1/48400.Finally, GCF of Fractions for 34/25, 45/16, 588/968 is 1/48400.