GCF of 324/40, 684/101
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/40, 684/101 i.e 36/4040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/40, 684/101.
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 324/40,684/101?
Given fractions are 324/40,684/101
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 324/40,684/101, numerators are 324,684
Denominators are 40,101
The GCF of 324,684 is 36 .
LCM of 40,101 is 4040.
The greatest common factor of 324/40,684/101 = [GCF of 324,684]/[LCM of 40,101]= 36/4040
Therefore, the GCF of 324/40,684/101 is 36/4040.
To find the highest common factor of 324,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 324,684 is 36.
Lets's calculate GCF of 324,684
| 2 | 324, 684 |
| 2 | 162, 342 |
| 3 | 81, 171 |
| 3 | 27, 57 |
| 9, 19 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 324,684 By Matching Biggest Common Factor Method
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 324,684 . The biggest common factor number is the GCF number.
So the greatest common factor 324,684 is 36.
Lets's calculate LCM of 40,101
Given numbers has no common factors except 1. So, there LCM is their product i.e 4040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/4040
Therefore, the GCF of Fractions 324/40,684/101 is 36/4040
Least Common Multiple of 40,101 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 40,101 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,101) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(40,101) x common factors =1 x 1 = 1
LCM(40,101) = ( 40 × 101 ) / 1
LCM(40,101) = 4040 / 1
LCM(40,101) = 4040
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 324/40, 684/101
1. What is the HCF of 324,684?
The HCF of 324,684 is 36
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 324/40, 684/101?
Answer: GCF of Numerators as per given numbers 324/40, 684/101 is
GCF of Numerators i.e. for 324,684 is 36
LCM of denominators i.e. for 40,101 is 4040.
Thus, GCF of Fractions is 36/4040.Finally, GCF of Fractions for 324/40, 684/101 is 36/4040.