GCF of 515/96, 420/264
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 515/96, 420/264 i.e 5/1056 easily. The following is the detailed procedure to determine the greatest common factor of fractions 515/96, 420/264.
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 515/96,420/264?
Given fractions are 515/96,420/264
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 515/96,420/264, numerators are 515,420
Denominators are 96,264
The GCF of 515,420 is 5 .
LCM of 96,264 is 1056.
The greatest common factor of 515/96,420/264 = [GCF of 515,420]/[LCM of 96,264]= 5/1056
Therefore, the GCF of 515/96,420/264 is 5/1056.
To find the highest common factor of 515,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 515 are 1, 5, 103, 515
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 515,420 is 5.
Lets's calculate GCF of 515,420
| 5 | 515, 420 |
| 103, 84 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 515,420 By Matching Biggest Common Factor Method
Now, list down the factors of 515
:1,5,103,515
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 515,420 . The biggest common factor number is the GCF number.
So the greatest common factor 515,420 is 5.
Lets's calculate LCM of 96,264
| 2 | 96, 264 |
| 2 | 48, 132 |
| 2 | 24, 66 |
| 3 | 12, 33 |
| 4, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 4 x 11 = 1056
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1056
Therefore, the GCF of Fractions 515/96,420/264 is 5/1056
Least Common Multiple of 96,264 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 96,264 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,264) = 24
common factors(in case of two or more numbers have common factors) = 1
GCF(96,264) x common factors =24 x 1 = 24
LCM(96,264) = ( 96 × 264 ) / 24
LCM(96,264) = 25344 / 24
LCM(96,264) = 1056
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 515/96, 420/264
1. What is the HCF of 515,420?
The HCF of 515,420 is 5
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 515/96, 420/264?
Answer: GCF of Numerators as per given numbers 515/96, 420/264 is
GCF of Numerators i.e. for 515,420 is 5
LCM of denominators i.e. for 96,264 is 1056.
Thus, GCF of Fractions is 5/1056.Finally, GCF of Fractions for 515/96, 420/264 is 5/1056.