GCF of 9216/320, 7314/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9216/320, 7314/420 i.e 6/6720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9216/320, 7314/420.
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 9216/320,7314/420?
Given fractions are 9216/320,7314/420
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 9216/320,7314/420, numerators are 9216,7314
Denominators are 320,420
The GCF of 9216,7314 is 6 .
LCM of 320,420 is 6720.
The greatest common factor of 9216/320,7314/420 = [GCF of 9216,7314]/[LCM of 320,420]= 6/6720
Therefore, the GCF of 9216/320,7314/420 is 6/6720.
To find the highest common factor of 9216,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 9216 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2304, 3072, 4608, 9216
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 9216,7314 is 6.
Lets's calculate GCF of 9216,7314
| 2 | 9216, 7314 |
| 3 | 4608, 3657 |
| 1536, 1219 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 9216,7314 By Matching Biggest Common Factor Method
Now, list down the factors of 9216
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,128,144,192,256,288,384,512,576,768,1024,1152,1536,2304,3072,4608,9216
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 9216,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 9216,7314 is 6.
Lets's calculate LCM of 320,420
| 2 | 320, 420 |
| 2 | 160, 210 |
| 5 | 80, 105 |
| 16, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 16 x 21 = 6720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/6720
Therefore, the GCF of Fractions 9216/320,7314/420 is 6/6720
Least Common Multiple of 320,420 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 320,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,420) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(320,420) x common factors =20 x 1 = 20
LCM(320,420) = ( 320 × 420 ) / 20
LCM(320,420) = 134400 / 20
LCM(320,420) = 6720
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FAQs on GCF of Fractions of 9216/320, 7314/420
1. What is the HCF of 9216,7314?
The HCF of 9216,7314 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 9216/320, 7314/420?
Answer: GCF of Numerators as per given numbers 9216/320, 7314/420 is
GCF of Numerators i.e. for 9216,7314 is 6
LCM of denominators i.e. for 320,420 is 6720.
Thus, GCF of Fractions is 6/6720.Finally, GCF of Fractions for 9216/320, 7314/420 is 6/6720.