GCF of 8528/320, 5405/7168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8528/320, 5405/7168 i.e 1/35840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8528/320, 5405/7168.
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 8528/320,5405/7168?
Given fractions are 8528/320,5405/7168
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 8528/320,5405/7168, numerators are 8528,5405
Denominators are 320,7168
The GCF of 8528,5405 is 1 .
LCM of 320,7168 is 35840.
The greatest common factor of 8528/320,5405/7168 = [GCF of 8528,5405]/[LCM of 320,7168]= 1/35840
Therefore, the GCF of 8528/320,5405/7168 is 1/35840.
To find the highest common factor of 8528,5405, we have to find the factors of both numbers and list the highest common factor.
The factors of 8528 are 1, 2, 4, 8, 13, 16, 26, 41, 52, 82, 104, 164, 208, 328, 533, 656, 1066, 2132, 4264, 8528
The factors of 5405 are 1, 5, 23, 47, 115, 235, 1081, 5405
The HCF of 8528,5405 is 1.
Lets's calculate GCF of 8528,5405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8528,5405 By Matching Biggest Common Factor Method
Now, list down the factors of 8528
:1,2,4,8,13,16,26,41,52,82,104,164,208,328,533,656,1066,2132,4264,8528
Now, list down the factors of 5405
:1,5,23,47,115,235,1081,5405
Greatest Common Factor
We found the factors 8528,5405 . The biggest common factor number is the GCF number.
So the greatest common factor 8528,5405 is 1.
Lets's calculate LCM of 320,7168
| 2 | 320, 7168 |
| 2 | 160, 3584 |
| 2 | 80, 1792 |
| 2 | 40, 896 |
| 2 | 20, 448 |
| 2 | 10, 224 |
| 5, 112 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 5 x 112 = 35840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35840
Therefore, the GCF of Fractions 8528/320,5405/7168 is 1/35840
Least Common Multiple of 320,7168 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 320,7168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,7168) = 64
common factors(in case of two or more numbers have common factors) = 1
GCF(320,7168) x common factors =64 x 1 = 64
LCM(320,7168) = ( 320 × 7168 ) / 64
LCM(320,7168) = 2293760 / 64
LCM(320,7168) = 35840
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FAQs on GCF of Fractions of 8528/320, 5405/7168
1. What is the HCF of 8528,5405?
The HCF of 8528,5405 is 1
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 8528/320, 5405/7168?
Answer: GCF of Numerators as per given numbers 8528/320, 5405/7168 is
GCF of Numerators i.e. for 8528,5405 is 1
LCM of denominators i.e. for 320,7168 is 35840.
Thus, GCF of Fractions is 1/35840.Finally, GCF of Fractions for 8528/320, 5405/7168 is 1/35840.