GCF of 152/16, 205/878
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 152/16, 205/878 i.e 1/7024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 152/16, 205/878.
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 152/16,205/878?
Given fractions are 152/16,205/878
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 152/16,205/878, numerators are 152,205
Denominators are 16,878
The GCF of 152,205 is 1 .
LCM of 16,878 is 7024.
The greatest common factor of 152/16,205/878 = [GCF of 152,205]/[LCM of 16,878]= 1/7024
Therefore, the GCF of 152/16,205/878 is 1/7024.
To find the highest common factor of 152,205, we have to find the factors of both numbers and list the highest common factor.
The factors of 152 are 1, 2, 4, 8, 19, 38, 76, 152
The factors of 205 are 1, 5, 41, 205
The HCF of 152,205 is 1.
Lets's calculate GCF of 152,205
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 152,205 By Matching Biggest Common Factor Method
Now, list down the factors of 152
:1,2,4,8,19,38,76,152
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 152,205 . The biggest common factor number is the GCF number.
So the greatest common factor 152,205 is 1.
Lets's calculate LCM of 16,878
| 2 | 16, 878 |
| 8, 439 |
∴ So the LCM of the given numbers is 2 x 8 x 439 = 7024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7024
Therefore, the GCF of Fractions 152/16,205/878 is 1/7024
Least Common Multiple of 16,878 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 16,878 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,878) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(16,878) x common factors =2 x 1 = 2
LCM(16,878) = ( 16 × 878 ) / 2
LCM(16,878) = 14048 / 2
LCM(16,878) = 7024
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FAQs on GCF of Fractions of 152/16, 205/878
1. What is the HCF of 152,205?
The HCF of 152,205 is 1
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 152/16, 205/878?
Answer: GCF of Numerators as per given numbers 152/16, 205/878 is
GCF of Numerators i.e. for 152,205 is 1
LCM of denominators i.e. for 16,878 is 7024.
Thus, GCF of Fractions is 1/7024.Finally, GCF of Fractions for 152/16, 205/878 is 1/7024.