GCF of 5/32, 10/37, 69/689, 509/860
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5/32, 10/37, 69/689, 509/860 i.e 1/175391840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5/32, 10/37, 69/689, 509/860.
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 5/32,10/37,69/689,509/860?
Given fractions are 5/32,10/37,69/689,509/860
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 5/32,10/37,69/689,509/860, numerators are 5,10,69,509
Denominators are 32,37,689,860
The GCF of 5,10,69,509 is 1 .
LCM of 32,37,689,860 is 175391840.
The greatest common factor of 5/32,10/37,69/689,509/860 = [GCF of 5,10,69,509]/[LCM of 32,37,689,860]= 1/175391840
Therefore, the GCF of 5/32,10/37,69/689,509/860 is 1/175391840.
To find the highest common factor of 5,10,69,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 5 are 1, 5
The factors of 10 are 1, 2, 5, 10
The factors of 69 are 1, 3, 23, 69
The factors of 509 are 1, 509
The HCF of 5,10,69,509 is 1.
Lets's calculate GCF of 5,10,69,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 5,10,69,509 By Matching Biggest Common Factor Method
Now, list down the factors of 5
:1,5
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 5,10,69,509 . The biggest common factor number is the GCF number.
So the greatest common factor 5,10,69,509 is 1.
Lets's calculate LCM of 32,37,689,860
| 2 | 32, 37, 689, 860 |
| 2 | 16, 37, 689, 430 |
| 8, 37, 689, 215 |
∴ So the LCM of the given numbers is 2 x 2 x 8 x 37 x 689 x 215 = 175391840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/175391840
Therefore, the GCF of Fractions 5/32,10/37,69/689,509/860 is 1/175391840
Least Common Multiple of 32,37,689,860 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 32,37,689,860 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,37,689,860) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(32,37,689,860) x common factors =1 x 4 = 4
LCM(32,37,689,860) = ( 32 × 37 × 689 × 860 ) / 4
LCM(32,37,689,860) = 701567360 / 4
LCM(32,37,689,860) = 175391840
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 5/32, 10/37, 69/689, 509/860
1. What is the HCF of 5,10,69,509?
The HCF of 5,10,69,509 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 5/32, 10/37, 69/689, 509/860?
Answer: GCF of Numerators as per given numbers 5/32, 10/37, 69/689, 509/860 is
GCF of Numerators i.e. for 5,10,69,509 is 1
LCM of denominators i.e. for 32,37,689,860 is 175391840.
Thus, GCF of Fractions is 1/175391840.Finally, GCF of Fractions for 5/32, 10/37, 69/689, 509/860 is 1/175391840.