GCF of 219/90, 321/12, 805/71
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 219/90, 321/12, 805/71 i.e 1/12780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 219/90, 321/12, 805/71.
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 219/90,321/12,805/71?
Given fractions are 219/90,321/12,805/71
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 219/90,321/12,805/71, numerators are 219,321,805
Denominators are 90,12,71
The GCF of 219,321,805 is 1 .
LCM of 90,12,71 is 12780.
The greatest common factor of 219/90,321/12,805/71 = [GCF of 219,321,805]/[LCM of 90,12,71]= 1/12780
Therefore, the GCF of 219/90,321/12,805/71 is 1/12780.
To find the highest common factor of 219,321,805, we have to find the factors of both numbers and list the highest common factor.
The factors of 219 are 1, 3, 73, 219
The factors of 321 are 1, 3, 107, 321
The factors of 805 are 1, 5, 7, 23, 35, 115, 161, 805
The HCF of 219,321,805 is 1.
Lets's calculate GCF of 219,321,805
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 219,321,805 By Matching Biggest Common Factor Method
Now, list down the factors of 219
:1,3,73,219
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 805
:1,5,7,23,35,115,161,805
Greatest Common Factor
We found the factors 219,321,805 . The biggest common factor number is the GCF number.
So the greatest common factor 219,321,805 is 1.
Lets's calculate LCM of 90,12,71
| 2 | 90, 12, 71 |
| 3 | 45, 6, 71 |
| 15, 2, 71 |
∴ So the LCM of the given numbers is 2 x 3 x 15 x 2 x 71 = 12780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12780
Therefore, the GCF of Fractions 219/90,321/12,805/71 is 1/12780
Least Common Multiple of 90,12,71 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 90,12,71 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,12,71) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(90,12,71) x common factors =1 x 6 = 6
LCM(90,12,71) = ( 90 × 12 × 71 ) / 6
LCM(90,12,71) = 76680 / 6
LCM(90,12,71) = 12780
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FAQs on GCF of Fractions of 219/90, 321/12, 805/71
1. What is the HCF of 219,321,805?
The HCF of 219,321,805 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 219/90, 321/12, 805/71?
Answer: GCF of Numerators as per given numbers 219/90, 321/12, 805/71 is
GCF of Numerators i.e. for 219,321,805 is 1
LCM of denominators i.e. for 90,12,71 is 12780.
Thus, GCF of Fractions is 1/12780.Finally, GCF of Fractions for 219/90, 321/12, 805/71 is 1/12780.