GCF of 519/42, 465/456
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 519/42, 465/456 i.e 3/3192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 519/42, 465/456.
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 519/42,465/456?
Given fractions are 519/42,465/456
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 519/42,465/456, numerators are 519,465
Denominators are 42,456
The GCF of 519,465 is 3 .
LCM of 42,456 is 3192.
The greatest common factor of 519/42,465/456 = [GCF of 519,465]/[LCM of 42,456]= 3/3192
Therefore, the GCF of 519/42,465/456 is 3/3192.
To find the highest common factor of 519,465, we have to find the factors of both numbers and list the highest common factor.
The factors of 519 are 1, 3, 173, 519
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 519,465 is 3.
Lets's calculate GCF of 519,465
| 3 | 519, 465 |
| 173, 155 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 519,465 By Matching Biggest Common Factor Method
Now, list down the factors of 519
:1,3,173,519
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 519,465 . The biggest common factor number is the GCF number.
So the greatest common factor 519,465 is 3.
Lets's calculate LCM of 42,456
| 2 | 42, 456 |
| 3 | 21, 228 |
| 7, 76 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 76 = 3192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3192
Therefore, the GCF of Fractions 519/42,465/456 is 3/3192
Least Common Multiple of 42,456 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 42,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,456) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,456) x common factors =6 x 1 = 6
LCM(42,456) = ( 42 × 456 ) / 6
LCM(42,456) = 19152 / 6
LCM(42,456) = 3192
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FAQs on GCF of Fractions of 519/42, 465/456
1. What is the HCF of 519,465?
The HCF of 519,465 is 3
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 519/42, 465/456?
Answer: GCF of Numerators as per given numbers 519/42, 465/456 is
GCF of Numerators i.e. for 519,465 is 3
LCM of denominators i.e. for 42,456 is 3192.
Thus, GCF of Fractions is 3/3192.Finally, GCF of Fractions for 519/42, 465/456 is 3/3192.