GCF of 7353/509, 7138/6421
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7353/509, 7138/6421 i.e 43/3268289 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7353/509, 7138/6421.
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 7353/509,7138/6421?
Given fractions are 7353/509,7138/6421
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 7353/509,7138/6421, numerators are 7353,7138
Denominators are 509,6421
The GCF of 7353,7138 is 43 .
LCM of 509,6421 is 3268289.
The greatest common factor of 7353/509,7138/6421 = [GCF of 7353,7138]/[LCM of 509,6421]= 43/3268289
Therefore, the GCF of 7353/509,7138/6421 is 43/3268289.
To find the highest common factor of 7353,7138, we have to find the factors of both numbers and list the highest common factor.
The factors of 7353 are 1, 3, 9, 19, 43, 57, 129, 171, 387, 817, 2451, 7353
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The HCF of 7353,7138 is 43.
Lets's calculate GCF of 7353,7138
| 43 | 7353, 7138 |
| 171, 166 |
∴ So the GCF of the given numbers is 43 = 43
Greatest Common Factor of 7353,7138 By Matching Biggest Common Factor Method
Now, list down the factors of 7353
:1,3,9,19,43,57,129,171,387,817,2451,7353
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Greatest Common Factor
We found the factors 7353,7138 . The biggest common factor number is the GCF number.
So the greatest common factor 7353,7138 is 43.
Lets's calculate LCM of 509,6421
Given numbers has no common factors except 1. So, there LCM is their product i.e 3268289
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 43/3268289
Therefore, the GCF of Fractions 7353/509,7138/6421 is 43/3268289
Least Common Multiple of 509,6421 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 509,6421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,6421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,6421) x common factors =1 x 1 = 1
LCM(509,6421) = ( 509 × 6421 ) / 1
LCM(509,6421) = 3268289 / 1
LCM(509,6421) = 3268289
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FAQs on GCF of Fractions of 7353/509, 7138/6421
1. What is the HCF of 7353,7138?
The HCF of 7353,7138 is 43
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 7353/509, 7138/6421?
Answer: GCF of Numerators as per given numbers 7353/509, 7138/6421 is
GCF of Numerators i.e. for 7353,7138 is 43
LCM of denominators i.e. for 509,6421 is 3268289.
Thus, GCF of Fractions is 43/3268289.Finally, GCF of Fractions for 7353/509, 7138/6421 is 43/3268289.