GCF of 4172/582, 7140/5846
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4172/582, 7140/5846 i.e 28/1701186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4172/582, 7140/5846.
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 4172/582,7140/5846?
Given fractions are 4172/582,7140/5846
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 4172/582,7140/5846, numerators are 4172,7140
Denominators are 582,5846
The GCF of 4172,7140 is 28 .
LCM of 582,5846 is 1701186.
The greatest common factor of 4172/582,7140/5846 = [GCF of 4172,7140]/[LCM of 582,5846]= 28/1701186
Therefore, the GCF of 4172/582,7140/5846 is 28/1701186.
To find the highest common factor of 4172,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 4172 are 1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086, 4172
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The HCF of 4172,7140 is 28.
Lets's calculate GCF of 4172,7140
| 2 | 4172, 7140 |
| 2 | 2086, 3570 |
| 7 | 1043, 1785 |
| 149, 255 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 4172,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 4172
:1,2,4,7,14,28,149,298,596,1043,2086,4172
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Greatest Common Factor
We found the factors 4172,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 4172,7140 is 28.
Lets's calculate LCM of 582,5846
| 2 | 582, 5846 |
| 291, 2923 |
∴ So the LCM of the given numbers is 2 x 291 x 2923 = 1701186
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/1701186
Therefore, the GCF of Fractions 4172/582,7140/5846 is 28/1701186
Least Common Multiple of 582,5846 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 582,5846 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(582,5846) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(582,5846) x common factors =2 x 1 = 2
LCM(582,5846) = ( 582 × 5846 ) / 2
LCM(582,5846) = 3402372 / 2
LCM(582,5846) = 1701186
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FAQs on GCF of Fractions of 4172/582, 7140/5846
1. What is the HCF of 4172,7140?
The HCF of 4172,7140 is 28
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 4172/582, 7140/5846?
Answer: GCF of Numerators as per given numbers 4172/582, 7140/5846 is
GCF of Numerators i.e. for 4172,7140 is 28
LCM of denominators i.e. for 582,5846 is 1701186.
Thus, GCF of Fractions is 28/1701186.Finally, GCF of Fractions for 4172/582, 7140/5846 is 28/1701186.