GCF of 683/828, 405/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 683/828, 405/420 i.e 1/28980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 683/828, 405/420.
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 683/828,405/420?
Given fractions are 683/828,405/420
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 683/828,405/420, numerators are 683,405
Denominators are 828,420
The GCF of 683,405 is 1 .
LCM of 828,420 is 28980.
The greatest common factor of 683/828,405/420 = [GCF of 683,405]/[LCM of 828,420]= 1/28980
Therefore, the GCF of 683/828,405/420 is 1/28980.
To find the highest common factor of 683,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 683 are 1, 683
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 683,405 is 1.
Lets's calculate GCF of 683,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 683,405 By Matching Biggest Common Factor Method
Now, list down the factors of 683
:1,683
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 683,405 . The biggest common factor number is the GCF number.
So the greatest common factor 683,405 is 1.
Lets's calculate LCM of 828,420
| 2 | 828, 420 |
| 2 | 414, 210 |
| 3 | 207, 105 |
| 69, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 69 x 35 = 28980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28980
Therefore, the GCF of Fractions 683/828,405/420 is 1/28980
Least Common Multiple of 828,420 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 828,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,420) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(828,420) x common factors =12 x 1 = 12
LCM(828,420) = ( 828 × 420 ) / 12
LCM(828,420) = 347760 / 12
LCM(828,420) = 28980
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FAQs on GCF of Fractions of 683/828, 405/420
1. What is the HCF of 683,405?
The HCF of 683,405 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 683/828, 405/420?
Answer: GCF of Numerators as per given numbers 683/828, 405/420 is
GCF of Numerators i.e. for 683,405 is 1
LCM of denominators i.e. for 828,420 is 28980.
Thus, GCF of Fractions is 1/28980.Finally, GCF of Fractions for 683/828, 405/420 is 1/28980.