GCF of 1059/854, 3084/5730
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1059/854, 3084/5730 i.e 3/2446710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1059/854, 3084/5730.
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 1059/854,3084/5730?
Given fractions are 1059/854,3084/5730
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 1059/854,3084/5730, numerators are 1059,3084
Denominators are 854,5730
The GCF of 1059,3084 is 3 .
LCM of 854,5730 is 2446710.
The greatest common factor of 1059/854,3084/5730 = [GCF of 1059,3084]/[LCM of 854,5730]= 3/2446710
Therefore, the GCF of 1059/854,3084/5730 is 3/2446710.
To find the highest common factor of 1059,3084, we have to find the factors of both numbers and list the highest common factor.
The factors of 1059 are 1, 3, 353, 1059
The factors of 3084 are 1, 2, 3, 4, 6, 12, 257, 514, 771, 1028, 1542, 3084
The HCF of 1059,3084 is 3.
Lets's calculate GCF of 1059,3084
| 3 | 1059, 3084 |
| 353, 1028 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1059,3084 By Matching Biggest Common Factor Method
Now, list down the factors of 1059
:1,3,353,1059
Now, list down the factors of 3084
:1,2,3,4,6,12,257,514,771,1028,1542,3084
Greatest Common Factor
We found the factors 1059,3084 . The biggest common factor number is the GCF number.
So the greatest common factor 1059,3084 is 3.
Lets's calculate LCM of 854,5730
| 2 | 854, 5730 |
| 427, 2865 |
∴ So the LCM of the given numbers is 2 x 427 x 2865 = 2446710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2446710
Therefore, the GCF of Fractions 1059/854,3084/5730 is 3/2446710
Least Common Multiple of 854,5730 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 854,5730 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,5730) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(854,5730) x common factors =2 x 1 = 2
LCM(854,5730) = ( 854 × 5730 ) / 2
LCM(854,5730) = 4893420 / 2
LCM(854,5730) = 2446710
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FAQs on GCF of Fractions of 1059/854, 3084/5730
1. What is the HCF of 1059,3084?
The HCF of 1059,3084 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 1059/854, 3084/5730?
Answer: GCF of Numerators as per given numbers 1059/854, 3084/5730 is
GCF of Numerators i.e. for 1059,3084 is 3
LCM of denominators i.e. for 854,5730 is 2446710.
Thus, GCF of Fractions is 3/2446710.Finally, GCF of Fractions for 1059/854, 3084/5730 is 3/2446710.