GCF of 7021/768, 5509/2008
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7021/768, 5509/2008 i.e 7/192768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7021/768, 5509/2008.
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 7021/768,5509/2008?
Given fractions are 7021/768,5509/2008
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 7021/768,5509/2008, numerators are 7021,5509
Denominators are 768,2008
The GCF of 7021,5509 is 7 .
LCM of 768,2008 is 192768.
The greatest common factor of 7021/768,5509/2008 = [GCF of 7021,5509]/[LCM of 768,2008]= 7/192768
Therefore, the GCF of 7021/768,5509/2008 is 7/192768.
To find the highest common factor of 7021,5509, we have to find the factors of both numbers and list the highest common factor.
The factors of 7021 are 1, 7, 17, 59, 119, 413, 1003, 7021
The factors of 5509 are 1, 7, 787, 5509
The HCF of 7021,5509 is 7.
Lets's calculate GCF of 7021,5509
| 7 | 7021, 5509 |
| 1003, 787 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 7021,5509 By Matching Biggest Common Factor Method
Now, list down the factors of 7021
:1,7,17,59,119,413,1003,7021
Now, list down the factors of 5509
:1,7,787,5509
Greatest Common Factor
We found the factors 7021,5509 . The biggest common factor number is the GCF number.
So the greatest common factor 7021,5509 is 7.
Lets's calculate LCM of 768,2008
| 2 | 768, 2008 |
| 2 | 384, 1004 |
| 2 | 192, 502 |
| 96, 251 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 96 x 251 = 192768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/192768
Therefore, the GCF of Fractions 7021/768,5509/2008 is 7/192768
Least Common Multiple of 768,2008 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 768,2008 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,2008) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(768,2008) x common factors =8 x 1 = 8
LCM(768,2008) = ( 768 × 2008 ) / 8
LCM(768,2008) = 1542144 / 8
LCM(768,2008) = 192768
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FAQs on GCF of Fractions of 7021/768, 5509/2008
1. What is the HCF of 7021,5509?
The HCF of 7021,5509 is 7
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 7021/768, 5509/2008?
Answer: GCF of Numerators as per given numbers 7021/768, 5509/2008 is
GCF of Numerators i.e. for 7021,5509 is 7
LCM of denominators i.e. for 768,2008 is 192768.
Thus, GCF of Fractions is 7/192768.Finally, GCF of Fractions for 7021/768, 5509/2008 is 7/192768.