GCF of 166/420, 133/960
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 166/420, 133/960 i.e 1/6720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 166/420, 133/960.
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 166/420,133/960?
Given fractions are 166/420,133/960
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 166/420,133/960, numerators are 166,133
Denominators are 420,960
The GCF of 166,133 is 1 .
LCM of 420,960 is 6720.
The greatest common factor of 166/420,133/960 = [GCF of 166,133]/[LCM of 420,960]= 1/6720
Therefore, the GCF of 166/420,133/960 is 1/6720.
To find the highest common factor of 166,133, we have to find the factors of both numbers and list the highest common factor.
The factors of 166 are 1, 2, 83, 166
The factors of 133 are 1, 7, 19, 133
The HCF of 166,133 is 1.
Lets's calculate GCF of 166,133
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 166,133 By Matching Biggest Common Factor Method
Now, list down the factors of 166
:1,2,83,166
Now, list down the factors of 133
:1,7,19,133
Greatest Common Factor
We found the factors 166,133 . The biggest common factor number is the GCF number.
So the greatest common factor 166,133 is 1.
Lets's calculate LCM of 420,960
| 2 | 420, 960 |
| 2 | 210, 480 |
| 3 | 105, 240 |
| 5 | 35, 80 |
| 7, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 16 = 6720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6720
Therefore, the GCF of Fractions 166/420,133/960 is 1/6720
Least Common Multiple of 420,960 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 420,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,960) = 60
common factors(in case of two or more numbers have common factors) = 1
GCF(420,960) x common factors =60 x 1 = 60
LCM(420,960) = ( 420 × 960 ) / 60
LCM(420,960) = 403200 / 60
LCM(420,960) = 6720
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FAQs on GCF of Fractions of 166/420, 133/960
1. What is the HCF of 166,133?
The HCF of 166,133 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 166/420, 133/960?
Answer: GCF of Numerators as per given numbers 166/420, 133/960 is
GCF of Numerators i.e. for 166,133 is 1
LCM of denominators i.e. for 420,960 is 6720.
Thus, GCF of Fractions is 1/6720.Finally, GCF of Fractions for 166/420, 133/960 is 1/6720.