GCF of 280/509, 455/546, 687/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 280/509, 455/546, 687/749 i.e 1/29736798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/509, 455/546, 687/749.
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 280/509,455/546,687/749?
Given fractions are 280/509,455/546,687/749
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 280/509,455/546,687/749, numerators are 280,455,687
Denominators are 509,546,749
The GCF of 280,455,687 is 1 .
LCM of 509,546,749 is 29736798.
The greatest common factor of 280/509,455/546,687/749 = [GCF of 280,455,687]/[LCM of 509,546,749]= 1/29736798
Therefore, the GCF of 280/509,455/546,687/749 is 1/29736798.
To find the highest common factor of 280,455,687, we have to find the factors of both numbers and list the highest common factor.
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The factors of 455 are 1, 5, 7, 13, 35, 65, 91, 455
The factors of 687 are 1, 3, 229, 687
The HCF of 280,455,687 is 1.
Lets's calculate GCF of 280,455,687
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 280,455,687 By Matching Biggest Common Factor Method
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Now, list down the factors of 455
:1,5,7,13,35,65,91,455
Now, list down the factors of 687
:1,3,229,687
Greatest Common Factor
We found the factors 280,455,687 . The biggest common factor number is the GCF number.
So the greatest common factor 280,455,687 is 1.
Lets's calculate LCM of 509,546,749
| 7 | 509, 546, 749 |
| 509, 78, 107 |
∴ So the LCM of the given numbers is 7 x 509 x 78 x 107 = 29736798
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29736798
Therefore, the GCF of Fractions 280/509,455/546,687/749 is 1/29736798
Least Common Multiple of 509,546,749 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 509,546,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,546,749) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(509,546,749) x common factors =1 x 7 = 7
LCM(509,546,749) = ( 509 × 546 × 749 ) / 7
LCM(509,546,749) = 208157586 / 7
LCM(509,546,749) = 29736798
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 280/509, 455/546, 687/749
1. What is the HCF of 280,455,687?
The HCF of 280,455,687 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 280/509, 455/546, 687/749?
Answer: GCF of Numerators as per given numbers 280/509, 455/546, 687/749 is
GCF of Numerators i.e. for 280,455,687 is 1
LCM of denominators i.e. for 509,546,749 is 29736798.
Thus, GCF of Fractions is 1/29736798.Finally, GCF of Fractions for 280/509, 455/546, 687/749 is 1/29736798.