GCF of 520/65, 369/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 520/65, 369/420 i.e 1/5460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/65, 369/420.
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 520/65,369/420?
Given fractions are 520/65,369/420
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 520/65,369/420, numerators are 520,369
Denominators are 65,420
The GCF of 520,369 is 1 .
LCM of 65,420 is 5460.
The greatest common factor of 520/65,369/420 = [GCF of 520,369]/[LCM of 65,420]= 1/5460
Therefore, the GCF of 520/65,369/420 is 1/5460.
To find the highest common factor of 520,369, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The factors of 369 are 1, 3, 9, 41, 123, 369
The HCF of 520,369 is 1.
Lets's calculate GCF of 520,369
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 520,369 By Matching Biggest Common Factor Method
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Now, list down the factors of 369
:1,3,9,41,123,369
Greatest Common Factor
We found the factors 520,369 . The biggest common factor number is the GCF number.
So the greatest common factor 520,369 is 1.
Lets's calculate LCM of 65,420
| 5 | 65, 420 |
| 13, 84 |
∴ So the LCM of the given numbers is 5 x 13 x 84 = 5460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5460
Therefore, the GCF of Fractions 520/65,369/420 is 1/5460
Least Common Multiple of 65,420 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 65,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,420) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,420) x common factors =5 x 1 = 5
LCM(65,420) = ( 65 × 420 ) / 5
LCM(65,420) = 27300 / 5
LCM(65,420) = 5460
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FAQs on GCF of Fractions of 520/65, 369/420
1. What is the HCF of 520,369?
The HCF of 520,369 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 520/65, 369/420?
Answer: GCF of Numerators as per given numbers 520/65, 369/420 is
GCF of Numerators i.e. for 520,369 is 1
LCM of denominators i.e. for 65,420 is 5460.
Thus, GCF of Fractions is 1/5460.Finally, GCF of Fractions for 520/65, 369/420 is 1/5460.