GCF of 633/10, 420/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 633/10, 420/409 i.e 3/4090 easily. The following is the detailed procedure to determine the greatest common factor of fractions 633/10, 420/409.
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 633/10,420/409?
Given fractions are 633/10,420/409
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 633/10,420/409, numerators are 633,420
Denominators are 10,409
The GCF of 633,420 is 3 .
LCM of 10,409 is 4090.
The greatest common factor of 633/10,420/409 = [GCF of 633,420]/[LCM of 10,409]= 3/4090
Therefore, the GCF of 633/10,420/409 is 3/4090.
To find the highest common factor of 633,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 633 are 1, 3, 211, 633
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 633,420 is 3.
Lets's calculate GCF of 633,420
| 3 | 633, 420 |
| 211, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 633,420 By Matching Biggest Common Factor Method
Now, list down the factors of 633
:1,3,211,633
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 633,420 . The biggest common factor number is the GCF number.
So the greatest common factor 633,420 is 3.
Lets's calculate LCM of 10,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 4090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4090
Therefore, the GCF of Fractions 633/10,420/409 is 3/4090
Least Common Multiple of 10,409 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 10,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(10,409) x common factors =1 x 1 = 1
LCM(10,409) = ( 10 × 409 ) / 1
LCM(10,409) = 4090 / 1
LCM(10,409) = 4090
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 633/10, 420/409
1. What is the HCF of 633,420?
The HCF of 633,420 is 3
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 633/10, 420/409?
Answer: GCF of Numerators as per given numbers 633/10, 420/409 is
GCF of Numerators i.e. for 633,420 is 3
LCM of denominators i.e. for 10,409 is 4090.
Thus, GCF of Fractions is 3/4090.Finally, GCF of Fractions for 633/10, 420/409 is 3/4090.