GCF of 75/34, 30/149, 345/504
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/34, 30/149, 345/504 i.e 15/1276632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/34, 30/149, 345/504.
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 75/34,30/149,345/504?
Given fractions are 75/34,30/149,345/504
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 75/34,30/149,345/504, numerators are 75,30,345
Denominators are 34,149,504
The GCF of 75,30,345 is 15 .
LCM of 34,149,504 is 1276632.
The greatest common factor of 75/34,30/149,345/504 = [GCF of 75,30,345]/[LCM of 34,149,504]= 15/1276632
Therefore, the GCF of 75/34,30/149,345/504 is 15/1276632.
To find the highest common factor of 75,30,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 75,30,345 is 15.
Lets's calculate GCF of 75,30,345
| 3 | 75, 30, 345 |
| 5 | 25, 10, 115 |
| 5, 2, 23 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 75,30,345 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 75,30,345 . The biggest common factor number is the GCF number.
So the greatest common factor 75,30,345 is 15.
Lets's calculate LCM of 34,149,504
| 2 | 34, 149, 504 |
| 17, 149, 252 |
∴ So the LCM of the given numbers is 2 x 17 x 149 x 252 = 1276632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/1276632
Therefore, the GCF of Fractions 75/34,30/149,345/504 is 15/1276632
Least Common Multiple of 34,149,504 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 34,149,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,149,504) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(34,149,504) x common factors =1 x 2 = 2
LCM(34,149,504) = ( 34 × 149 × 504 ) / 2
LCM(34,149,504) = 2553264 / 2
LCM(34,149,504) = 1276632
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 75/34, 30/149, 345/504
1. What is the HCF of 75,30,345?
The HCF of 75,30,345 is 15
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 75/34, 30/149, 345/504?
Answer: GCF of Numerators as per given numbers 75/34, 30/149, 345/504 is
GCF of Numerators i.e. for 75,30,345 is 15
LCM of denominators i.e. for 34,149,504 is 1276632.
Thus, GCF of Fractions is 15/1276632.Finally, GCF of Fractions for 75/34, 30/149, 345/504 is 15/1276632.