GCF of 999/114, 120/769
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 999/114, 120/769 i.e 3/87666 easily. The following is the detailed procedure to determine the greatest common factor of fractions 999/114, 120/769.
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 999/114,120/769?
Given fractions are 999/114,120/769
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 999/114,120/769, numerators are 999,120
Denominators are 114,769
The GCF of 999,120 is 3 .
LCM of 114,769 is 87666.
The greatest common factor of 999/114,120/769 = [GCF of 999,120]/[LCM of 114,769]= 3/87666
Therefore, the GCF of 999/114,120/769 is 3/87666.
To find the highest common factor of 999,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 999,120 is 3.
Lets's calculate GCF of 999,120
| 3 | 999, 120 |
| 333, 40 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 999,120 By Matching Biggest Common Factor Method
Now, list down the factors of 999
:1,3,9,27,37,111,333,999
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 999,120 . The biggest common factor number is the GCF number.
So the greatest common factor 999,120 is 3.
Lets's calculate LCM of 114,769
Given numbers has no common factors except 1. So, there LCM is their product i.e 87666
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/87666
Therefore, the GCF of Fractions 999/114,120/769 is 3/87666
Least Common Multiple of 114,769 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 114,769 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(114,769) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(114,769) x common factors =1 x 1 = 1
LCM(114,769) = ( 114 × 769 ) / 1
LCM(114,769) = 87666 / 1
LCM(114,769) = 87666
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FAQs on GCF of Fractions of 999/114, 120/769
1. What is the HCF of 999,120?
The HCF of 999,120 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 999/114, 120/769?
Answer: GCF of Numerators as per given numbers 999/114, 120/769 is
GCF of Numerators i.e. for 999,120 is 3
LCM of denominators i.e. for 114,769 is 87666.
Thus, GCF of Fractions is 3/87666.Finally, GCF of Fractions for 999/114, 120/769 is 3/87666.