GCF of 509/462, 546/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 509/462, 546/714 i.e 1/7854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 509/462, 546/714.
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 509/462,546/714?
Given fractions are 509/462,546/714
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 509/462,546/714, numerators are 509,546
Denominators are 462,714
The GCF of 509,546 is 1 .
LCM of 462,714 is 7854.
The greatest common factor of 509/462,546/714 = [GCF of 509,546]/[LCM of 462,714]= 1/7854
Therefore, the GCF of 509/462,546/714 is 1/7854.
To find the highest common factor of 509,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 509 are 1, 509
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 509,546 is 1.
Lets's calculate GCF of 509,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 509,546 By Matching Biggest Common Factor Method
Now, list down the factors of 509
:1,509
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 509,546 . The biggest common factor number is the GCF number.
So the greatest common factor 509,546 is 1.
Lets's calculate LCM of 462,714
| 2 | 462, 714 |
| 3 | 231, 357 |
| 7 | 77, 119 |
| 11, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 11 x 17 = 7854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7854
Therefore, the GCF of Fractions 509/462,546/714 is 1/7854
Least Common Multiple of 462,714 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 462,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,714) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(462,714) x common factors =42 x 1 = 42
LCM(462,714) = ( 462 × 714 ) / 42
LCM(462,714) = 329868 / 42
LCM(462,714) = 7854
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FAQs on GCF of Fractions of 509/462, 546/714
1. What is the HCF of 509,546?
The HCF of 509,546 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 509/462, 546/714?
Answer: GCF of Numerators as per given numbers 509/462, 546/714 is
GCF of Numerators i.e. for 509,546 is 1
LCM of denominators i.e. for 462,714 is 7854.
Thus, GCF of Fractions is 1/7854.Finally, GCF of Fractions for 509/462, 546/714 is 1/7854.