GCF of 1986/724, 9684/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1986/724, 9684/120 i.e 6/21720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1986/724, 9684/120.
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 1986/724,9684/120?
Given fractions are 1986/724,9684/120
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 1986/724,9684/120, numerators are 1986,9684
Denominators are 724,120
The GCF of 1986,9684 is 6 .
LCM of 724,120 is 21720.
The greatest common factor of 1986/724,9684/120 = [GCF of 1986,9684]/[LCM of 724,120]= 6/21720
Therefore, the GCF of 1986/724,9684/120 is 6/21720.
To find the highest common factor of 1986,9684, we have to find the factors of both numbers and list the highest common factor.
The factors of 1986 are 1, 2, 3, 6, 331, 662, 993, 1986
The factors of 9684 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 269, 538, 807, 1076, 1614, 2421, 3228, 4842, 9684
The HCF of 1986,9684 is 6.
Lets's calculate GCF of 1986,9684
| 2 | 1986, 9684 |
| 3 | 993, 4842 |
| 331, 1614 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1986,9684 By Matching Biggest Common Factor Method
Now, list down the factors of 1986
:1,2,3,6,331,662,993,1986
Now, list down the factors of 9684
:1,2,3,4,6,9,12,18,36,269,538,807,1076,1614,2421,3228,4842,9684
Greatest Common Factor
We found the factors 1986,9684 . The biggest common factor number is the GCF number.
So the greatest common factor 1986,9684 is 6.
Lets's calculate LCM of 724,120
| 2 | 724, 120 |
| 2 | 362, 60 |
| 181, 30 |
∴ So the LCM of the given numbers is 2 x 2 x 181 x 30 = 21720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/21720
Therefore, the GCF of Fractions 1986/724,9684/120 is 6/21720
Least Common Multiple of 724,120 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 724,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,120) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(724,120) x common factors =4 x 1 = 4
LCM(724,120) = ( 724 × 120 ) / 4
LCM(724,120) = 86880 / 4
LCM(724,120) = 21720
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1986/724, 9684/120
1. What is the HCF of 1986,9684?
The HCF of 1986,9684 is 6
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 1986/724, 9684/120?
Answer: GCF of Numerators as per given numbers 1986/724, 9684/120 is
GCF of Numerators i.e. for 1986,9684 is 6
LCM of denominators i.e. for 724,120 is 21720.
Thus, GCF of Fractions is 6/21720.Finally, GCF of Fractions for 1986/724, 9684/120 is 6/21720.