GCF of 61/410, 84/858, 585/820
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 61/410, 84/858, 585/820 i.e 1/351780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/410, 84/858, 585/820.
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 61/410,84/858,585/820?
Given fractions are 61/410,84/858,585/820
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 61/410,84/858,585/820, numerators are 61,84,585
Denominators are 410,858,820
The GCF of 61,84,585 is 1 .
LCM of 410,858,820 is 351780.
The greatest common factor of 61/410,84/858,585/820 = [GCF of 61,84,585]/[LCM of 410,858,820]= 1/351780
Therefore, the GCF of 61/410,84/858,585/820 is 1/351780.
To find the highest common factor of 61,84,585, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
The HCF of 61,84,585 is 1.
Lets's calculate GCF of 61,84,585
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 61,84,585 By Matching Biggest Common Factor Method
Now, list down the factors of 61
:1,61
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 585
:1,3,5,9,13,15,39,45,65,117,195,585
Greatest Common Factor
We found the factors 61,84,585 . The biggest common factor number is the GCF number.
So the greatest common factor 61,84,585 is 1.
Lets's calculate LCM of 410,858,820
| 2 | 410, 858, 820 |
| 5 | 205, 429, 410 |
| 41 | 41, 429, 82 |
| 1, 429, 2 |
∴ So the LCM of the given numbers is 2 x 5 x 41 x 1 x 429 x 2 = 351780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/351780
Therefore, the GCF of Fractions 61/410,84/858,585/820 is 1/351780
Least Common Multiple of 410,858,820 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 410,858,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(410,858,820) = 2
common factors(in case of two or more numbers have common factors) = 410
GCF(410,858,820) x common factors =2 x 410 = 820
LCM(410,858,820) = ( 410 × 858 × 820 ) / 820
LCM(410,858,820) = 288459600 / 820
LCM(410,858,820) = 351780
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 61/410, 84/858, 585/820
1. What is the HCF of 61,84,585?
The HCF of 61,84,585 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 61/410, 84/858, 585/820?
Answer: GCF of Numerators as per given numbers 61/410, 84/858, 585/820 is
GCF of Numerators i.e. for 61,84,585 is 1
LCM of denominators i.e. for 410,858,820 is 351780.
Thus, GCF of Fractions is 1/351780.Finally, GCF of Fractions for 61/410, 84/858, 585/820 is 1/351780.