GCF of 465/32, 219/6686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 465/32, 219/6686 i.e 3/106976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 465/32, 219/6686.
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 465/32,219/6686?
Given fractions are 465/32,219/6686
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 465/32,219/6686, numerators are 465,219
Denominators are 32,6686
The GCF of 465,219 is 3 .
LCM of 32,6686 is 106976.
The greatest common factor of 465/32,219/6686 = [GCF of 465,219]/[LCM of 32,6686]= 3/106976
Therefore, the GCF of 465/32,219/6686 is 3/106976.
To find the highest common factor of 465,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The factors of 219 are 1, 3, 73, 219
The HCF of 465,219 is 3.
Lets's calculate GCF of 465,219
| 3 | 465, 219 |
| 155, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 465,219 By Matching Biggest Common Factor Method
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 465,219 . The biggest common factor number is the GCF number.
So the greatest common factor 465,219 is 3.
Lets's calculate LCM of 32,6686
| 2 | 32, 6686 |
| 16, 3343 |
∴ So the LCM of the given numbers is 2 x 16 x 3343 = 106976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/106976
Therefore, the GCF of Fractions 465/32,219/6686 is 3/106976
Least Common Multiple of 32,6686 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 32,6686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,6686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,6686) x common factors =2 x 1 = 2
LCM(32,6686) = ( 32 × 6686 ) / 2
LCM(32,6686) = 213952 / 2
LCM(32,6686) = 106976
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FAQs on GCF of Fractions of 465/32, 219/6686
1. What is the HCF of 465,219?
The HCF of 465,219 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 465/32, 219/6686?
Answer: GCF of Numerators as per given numbers 465/32, 219/6686 is
GCF of Numerators i.e. for 465,219 is 3
LCM of denominators i.e. for 32,6686 is 106976.
Thus, GCF of Fractions is 3/106976.Finally, GCF of Fractions for 465/32, 219/6686 is 3/106976.