GCF of 1023/470, 9641/9730
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1023/470, 9641/9730 i.e 31/457310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1023/470, 9641/9730.
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 1023/470,9641/9730?
Given fractions are 1023/470,9641/9730
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 1023/470,9641/9730, numerators are 1023,9641
Denominators are 470,9730
The GCF of 1023,9641 is 31 .
LCM of 470,9730 is 457310.
The greatest common factor of 1023/470,9641/9730 = [GCF of 1023,9641]/[LCM of 470,9730]= 31/457310
Therefore, the GCF of 1023/470,9641/9730 is 31/457310.
To find the highest common factor of 1023,9641, we have to find the factors of both numbers and list the highest common factor.
The factors of 1023 are 1, 3, 11, 31, 33, 93, 341, 1023
The factors of 9641 are 1, 31, 311, 9641
The HCF of 1023,9641 is 31.
Lets's calculate GCF of 1023,9641
| 31 | 1023, 9641 |
| 33, 311 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 1023,9641 By Matching Biggest Common Factor Method
Now, list down the factors of 1023
:1,3,11,31,33,93,341,1023
Now, list down the factors of 9641
:1,31,311,9641
Greatest Common Factor
We found the factors 1023,9641 . The biggest common factor number is the GCF number.
So the greatest common factor 1023,9641 is 31.
Lets's calculate LCM of 470,9730
| 2 | 470, 9730 |
| 5 | 235, 4865 |
| 47, 973 |
∴ So the LCM of the given numbers is 2 x 5 x 47 x 973 = 457310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/457310
Therefore, the GCF of Fractions 1023/470,9641/9730 is 31/457310
Least Common Multiple of 470,9730 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 470,9730 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,9730) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(470,9730) x common factors =10 x 1 = 10
LCM(470,9730) = ( 470 × 9730 ) / 10
LCM(470,9730) = 4573100 / 10
LCM(470,9730) = 457310
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FAQs on GCF of Fractions of 1023/470, 9641/9730
1. What is the HCF of 1023,9641?
The HCF of 1023,9641 is 31
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 1023/470, 9641/9730?
Answer: GCF of Numerators as per given numbers 1023/470, 9641/9730 is
GCF of Numerators i.e. for 1023,9641 is 31
LCM of denominators i.e. for 470,9730 is 457310.
Thus, GCF of Fractions is 31/457310.Finally, GCF of Fractions for 1023/470, 9641/9730 is 31/457310.