GCF of 7250/586, 5840/2172
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7250/586, 5840/2172 i.e 10/636396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7250/586, 5840/2172.
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 7250/586,5840/2172?
Given fractions are 7250/586,5840/2172
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 7250/586,5840/2172, numerators are 7250,5840
Denominators are 586,2172
The GCF of 7250,5840 is 10 .
LCM of 586,2172 is 636396.
The greatest common factor of 7250/586,5840/2172 = [GCF of 7250,5840]/[LCM of 586,2172]= 10/636396
Therefore, the GCF of 7250/586,5840/2172 is 10/636396.
To find the highest common factor of 7250,5840, we have to find the factors of both numbers and list the highest common factor.
The factors of 7250 are 1, 2, 5, 10, 25, 29, 50, 58, 125, 145, 250, 290, 725, 1450, 3625, 7250
The factors of 5840 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 73, 80, 146, 292, 365, 584, 730, 1168, 1460, 2920, 5840
The HCF of 7250,5840 is 10.
Lets's calculate GCF of 7250,5840
| 2 | 7250, 5840 |
| 5 | 3625, 2920 |
| 725, 584 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 7250,5840 By Matching Biggest Common Factor Method
Now, list down the factors of 7250
:1,2,5,10,25,29,50,58,125,145,250,290,725,1450,3625,7250
Now, list down the factors of 5840
:1,2,4,5,8,10,16,20,40,73,80,146,292,365,584,730,1168,1460,2920,5840
Greatest Common Factor
We found the factors 7250,5840 . The biggest common factor number is the GCF number.
So the greatest common factor 7250,5840 is 10.
Lets's calculate LCM of 586,2172
| 2 | 586, 2172 |
| 293, 1086 |
∴ So the LCM of the given numbers is 2 x 293 x 1086 = 636396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/636396
Therefore, the GCF of Fractions 7250/586,5840/2172 is 10/636396
Least Common Multiple of 586,2172 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 586,2172 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,2172) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(586,2172) x common factors =2 x 1 = 2
LCM(586,2172) = ( 586 × 2172 ) / 2
LCM(586,2172) = 1272792 / 2
LCM(586,2172) = 636396
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FAQs on GCF of Fractions of 7250/586, 5840/2172
1. What is the HCF of 7250,5840?
The HCF of 7250,5840 is 10
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 7250/586, 5840/2172?
Answer: GCF of Numerators as per given numbers 7250/586, 5840/2172 is
GCF of Numerators i.e. for 7250,5840 is 10
LCM of denominators i.e. for 586,2172 is 636396.
Thus, GCF of Fractions is 10/636396.Finally, GCF of Fractions for 7250/586, 5840/2172 is 10/636396.