GCF of 870/546, 2005/178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 870/546, 2005/178 i.e 5/48594 easily. The following is the detailed procedure to determine the greatest common factor of fractions 870/546, 2005/178.
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 870/546,2005/178?
Given fractions are 870/546,2005/178
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 870/546,2005/178, numerators are 870,2005
Denominators are 546,178
The GCF of 870,2005 is 5 .
LCM of 546,178 is 48594.
The greatest common factor of 870/546,2005/178 = [GCF of 870,2005]/[LCM of 546,178]= 5/48594
Therefore, the GCF of 870/546,2005/178 is 5/48594.
To find the highest common factor of 870,2005, we have to find the factors of both numbers and list the highest common factor.
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The factors of 2005 are 1, 5, 401, 2005
The HCF of 870,2005 is 5.
Lets's calculate GCF of 870,2005
| 5 | 870, 2005 |
| 174, 401 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 870,2005 By Matching Biggest Common Factor Method
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Now, list down the factors of 2005
:1,5,401,2005
Greatest Common Factor
We found the factors 870,2005 . The biggest common factor number is the GCF number.
So the greatest common factor 870,2005 is 5.
Lets's calculate LCM of 546,178
| 2 | 546, 178 |
| 273, 89 |
∴ So the LCM of the given numbers is 2 x 273 x 89 = 48594
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/48594
Therefore, the GCF of Fractions 870/546,2005/178 is 5/48594
Least Common Multiple of 546,178 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 546,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(546,178) x common factors =2 x 1 = 2
LCM(546,178) = ( 546 × 178 ) / 2
LCM(546,178) = 97188 / 2
LCM(546,178) = 48594
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FAQs on GCF of Fractions of 870/546, 2005/178
1. What is the HCF of 870,2005?
The HCF of 870,2005 is 5
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 870/546, 2005/178?
Answer: GCF of Numerators as per given numbers 870/546, 2005/178 is
GCF of Numerators i.e. for 870,2005 is 5
LCM of denominators i.e. for 546,178 is 48594.
Thus, GCF of Fractions is 5/48594.Finally, GCF of Fractions for 870/546, 2005/178 is 5/48594.