GCF of 9982/532, 2002/1000
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9982/532, 2002/1000 i.e 14/133000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9982/532, 2002/1000.
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 9982/532,2002/1000?
Given fractions are 9982/532,2002/1000
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 9982/532,2002/1000, numerators are 9982,2002
Denominators are 532,1000
The GCF of 9982,2002 is 14 .
LCM of 532,1000 is 133000.
The greatest common factor of 9982/532,2002/1000 = [GCF of 9982,2002]/[LCM of 532,1000]= 14/133000
Therefore, the GCF of 9982/532,2002/1000 is 14/133000.
To find the highest common factor of 9982,2002, we have to find the factors of both numbers and list the highest common factor.
The factors of 9982 are 1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982
The factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002
The HCF of 9982,2002 is 14.
Lets's calculate GCF of 9982,2002
| 2 | 9982, 2002 |
| 7 | 4991, 1001 |
| 713, 143 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 9982,2002 By Matching Biggest Common Factor Method
Now, list down the factors of 9982
:1,2,7,14,23,31,46,62,161,217,322,434,713,1426,4991,9982
Now, list down the factors of 2002
:1,2,7,11,13,14,22,26,77,91,143,154,182,286,1001,2002
Greatest Common Factor
We found the factors 9982,2002 . The biggest common factor number is the GCF number.
So the greatest common factor 9982,2002 is 14.
Lets's calculate LCM of 532,1000
| 2 | 532, 1000 |
| 2 | 266, 500 |
| 133, 250 |
∴ So the LCM of the given numbers is 2 x 2 x 133 x 250 = 133000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/133000
Therefore, the GCF of Fractions 9982/532,2002/1000 is 14/133000
Least Common Multiple of 532,1000 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 532,1000 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(532,1000) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(532,1000) x common factors =4 x 1 = 4
LCM(532,1000) = ( 532 × 1000 ) / 4
LCM(532,1000) = 532000 / 4
LCM(532,1000) = 133000
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FAQs on GCF of Fractions of 9982/532, 2002/1000
1. What is the HCF of 9982,2002?
The HCF of 9982,2002 is 14
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 9982/532, 2002/1000?
Answer: GCF of Numerators as per given numbers 9982/532, 2002/1000 is
GCF of Numerators i.e. for 9982,2002 is 14
LCM of denominators i.e. for 532,1000 is 133000.
Thus, GCF of Fractions is 14/133000.Finally, GCF of Fractions for 9982/532, 2002/1000 is 14/133000.