GCF of 324/440, 9724/709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/440, 9724/709 i.e 4/311960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/440, 9724/709.
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 324/440,9724/709?
Given fractions are 324/440,9724/709
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 324/440,9724/709, numerators are 324,9724
Denominators are 440,709
The GCF of 324,9724 is 4 .
LCM of 440,709 is 311960.
The greatest common factor of 324/440,9724/709 = [GCF of 324,9724]/[LCM of 440,709]= 4/311960
Therefore, the GCF of 324/440,9724/709 is 4/311960.
To find the highest common factor of 324,9724, 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 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724
The HCF of 324,9724 is 4.
Lets's calculate GCF of 324,9724
| 2 | 324, 9724 |
| 2 | 162, 4862 |
| 81, 2431 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 324,9724 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 9724
:1,2,4,11,13,17,22,26,34,44,52,68,143,187,221,286,374,442,572,748,884,2431,4862,9724
Greatest Common Factor
We found the factors 324,9724 . The biggest common factor number is the GCF number.
So the greatest common factor 324,9724 is 4.
Lets's calculate LCM of 440,709
Given numbers has no common factors except 1. So, there LCM is their product i.e 311960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/311960
Therefore, the GCF of Fractions 324/440,9724/709 is 4/311960
Least Common Multiple of 440,709 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 440,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(440,709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(440,709) x common factors =1 x 1 = 1
LCM(440,709) = ( 440 × 709 ) / 1
LCM(440,709) = 311960 / 1
LCM(440,709) = 311960
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FAQs on GCF of Fractions of 324/440, 9724/709
1. What is the HCF of 324,9724?
The HCF of 324,9724 is 4
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 324/440, 9724/709?
Answer: GCF of Numerators as per given numbers 324/440, 9724/709 is
GCF of Numerators i.e. for 324,9724 is 4
LCM of denominators i.e. for 440,709 is 311960.
Thus, GCF of Fractions is 4/311960.Finally, GCF of Fractions for 324/440, 9724/709 is 4/311960.