GCF of 969/406, 966/305
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 969/406, 966/305 i.e 3/123830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 969/406, 966/305.
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 969/406,966/305?
Given fractions are 969/406,966/305
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 969/406,966/305, numerators are 969,966
Denominators are 406,305
The GCF of 969,966 is 3 .
LCM of 406,305 is 123830.
The greatest common factor of 969/406,966/305 = [GCF of 969,966]/[LCM of 406,305]= 3/123830
Therefore, the GCF of 969/406,966/305 is 3/123830.
To find the highest common factor of 969,966, we have to find the factors of both numbers and list the highest common factor.
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The HCF of 969,966 is 3.
Lets's calculate GCF of 969,966
| 3 | 969, 966 |
| 323, 322 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 969,966 By Matching Biggest Common Factor Method
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Greatest Common Factor
We found the factors 969,966 . The biggest common factor number is the GCF number.
So the greatest common factor 969,966 is 3.
Lets's calculate LCM of 406,305
Given numbers has no common factors except 1. So, there LCM is their product i.e 123830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/123830
Therefore, the GCF of Fractions 969/406,966/305 is 3/123830
Least Common Multiple of 406,305 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 406,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,305) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(406,305) x common factors =1 x 1 = 1
LCM(406,305) = ( 406 × 305 ) / 1
LCM(406,305) = 123830 / 1
LCM(406,305) = 123830
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FAQs on GCF of Fractions of 969/406, 966/305
1. What is the HCF of 969,966?
The HCF of 969,966 is 3
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 969/406, 966/305?
Answer: GCF of Numerators as per given numbers 969/406, 966/305 is
GCF of Numerators i.e. for 969,966 is 3
LCM of denominators i.e. for 406,305 is 123830.
Thus, GCF of Fractions is 3/123830.Finally, GCF of Fractions for 969/406, 966/305 is 3/123830.