GCF of 500/69, 658/405
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 500/69, 658/405 i.e 2/9315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/69, 658/405.
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 500/69,658/405?
Given fractions are 500/69,658/405
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 500/69,658/405, numerators are 500,658
Denominators are 69,405
The GCF of 500,658 is 2 .
LCM of 69,405 is 9315.
The greatest common factor of 500/69,658/405 = [GCF of 500,658]/[LCM of 69,405]= 2/9315
Therefore, the GCF of 500/69,658/405 is 2/9315.
To find the highest common factor of 500,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 500,658 is 2.
Lets's calculate GCF of 500,658
| 2 | 500, 658 |
| 250, 329 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 500,658 By Matching Biggest Common Factor Method
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 500,658 . The biggest common factor number is the GCF number.
So the greatest common factor 500,658 is 2.
Lets's calculate LCM of 69,405
| 3 | 69, 405 |
| 23, 135 |
∴ So the LCM of the given numbers is 3 x 23 x 135 = 9315
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9315
Therefore, the GCF of Fractions 500/69,658/405 is 2/9315
Least Common Multiple of 69,405 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 69,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,405) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,405) x common factors =3 x 1 = 3
LCM(69,405) = ( 69 × 405 ) / 3
LCM(69,405) = 27945 / 3
LCM(69,405) = 9315
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FAQs on GCF of Fractions of 500/69, 658/405
1. What is the HCF of 500,658?
The HCF of 500,658 is 2
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 500/69, 658/405?
Answer: GCF of Numerators as per given numbers 500/69, 658/405 is
GCF of Numerators i.e. for 500,658 is 2
LCM of denominators i.e. for 69,405 is 9315.
Thus, GCF of Fractions is 2/9315.Finally, GCF of Fractions for 500/69, 658/405 is 2/9315.