GCF of 174/65, 238/45, 870/48
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 174/65, 238/45, 870/48 i.e 2/9360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/65, 238/45, 870/48.
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 174/65,238/45,870/48?
Given fractions are 174/65,238/45,870/48
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 174/65,238/45,870/48, numerators are 174,238,870
Denominators are 65,45,48
The GCF of 174,238,870 is 2 .
LCM of 65,45,48 is 9360.
The greatest common factor of 174/65,238/45,870/48 = [GCF of 174,238,870]/[LCM of 65,45,48]= 2/9360
Therefore, the GCF of 174/65,238/45,870/48 is 2/9360.
To find the highest common factor of 174,238,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 174,238,870 is 2.
Lets's calculate GCF of 174,238,870
| 2 | 174, 238, 870 |
| 87, 119, 435 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 174,238,870 By Matching Biggest Common Factor Method
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 174,238,870 . The biggest common factor number is the GCF number.
So the greatest common factor 174,238,870 is 2.
Lets's calculate LCM of 65,45,48
| 3 | 65, 45, 48 |
| 5 | 65, 15, 16 |
| 13, 3, 16 |
∴ So the LCM of the given numbers is 3 x 5 x 13 x 3 x 16 = 9360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9360
Therefore, the GCF of Fractions 174/65,238/45,870/48 is 2/9360
Least Common Multiple of 65,45,48 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 65,45,48 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,45,48) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(65,45,48) x common factors =1 x 15 = 15
LCM(65,45,48) = ( 65 × 45 × 48 ) / 15
LCM(65,45,48) = 140400 / 15
LCM(65,45,48) = 9360
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FAQs on GCF of Fractions of 174/65, 238/45, 870/48
1. What is the HCF of 174,238,870?
The HCF of 174,238,870 is 2
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 174/65, 238/45, 870/48?
Answer: GCF of Numerators as per given numbers 174/65, 238/45, 870/48 is
GCF of Numerators i.e. for 174,238,870 is 2
LCM of denominators i.e. for 65,45,48 is 9360.
Thus, GCF of Fractions is 2/9360.Finally, GCF of Fractions for 174/65, 238/45, 870/48 is 2/9360.