GCF of 216/969, 5322/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 216/969, 5322/120 i.e 6/38760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/969, 5322/120.
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 216/969,5322/120?
Given fractions are 216/969,5322/120
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 216/969,5322/120, numerators are 216,5322
Denominators are 969,120
The GCF of 216,5322 is 6 .
LCM of 969,120 is 38760.
The greatest common factor of 216/969,5322/120 = [GCF of 216,5322]/[LCM of 969,120]= 6/38760
Therefore, the GCF of 216/969,5322/120 is 6/38760.
To find the highest common factor of 216,5322, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 5322 are 1, 2, 3, 6, 887, 1774, 2661, 5322
The HCF of 216,5322 is 6.
Lets's calculate GCF of 216,5322
| 2 | 216, 5322 |
| 3 | 108, 2661 |
| 36, 887 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 216,5322 By Matching Biggest Common Factor Method
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 5322
:1,2,3,6,887,1774,2661,5322
Greatest Common Factor
We found the factors 216,5322 . The biggest common factor number is the GCF number.
So the greatest common factor 216,5322 is 6.
Lets's calculate LCM of 969,120
| 3 | 969, 120 |
| 323, 40 |
∴ So the LCM of the given numbers is 3 x 323 x 40 = 38760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/38760
Therefore, the GCF of Fractions 216/969,5322/120 is 6/38760
Least Common Multiple of 969,120 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 969,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(969,120) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(969,120) x common factors =3 x 1 = 3
LCM(969,120) = ( 969 × 120 ) / 3
LCM(969,120) = 116280 / 3
LCM(969,120) = 38760
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 216/969, 5322/120
1. What is the HCF of 216,5322?
The HCF of 216,5322 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 216/969, 5322/120?
Answer: GCF of Numerators as per given numbers 216/969, 5322/120 is
GCF of Numerators i.e. for 216,5322 is 6
LCM of denominators i.e. for 969,120 is 38760.
Thus, GCF of Fractions is 6/38760.Finally, GCF of Fractions for 216/969, 5322/120 is 6/38760.