GCF of 2123/756, 2982/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2123/756, 2982/728 i.e 1/19656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2123/756, 2982/728.
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 2123/756,2982/728?
Given fractions are 2123/756,2982/728
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 2123/756,2982/728, numerators are 2123,2982
Denominators are 756,728
The GCF of 2123,2982 is 1 .
LCM of 756,728 is 19656.
The greatest common factor of 2123/756,2982/728 = [GCF of 2123,2982]/[LCM of 756,728]= 1/19656
Therefore, the GCF of 2123/756,2982/728 is 1/19656.
To find the highest common factor of 2123,2982, we have to find the factors of both numbers and list the highest common factor.
The factors of 2123 are 1, 11, 193, 2123
The factors of 2982 are 1, 2, 3, 6, 7, 14, 21, 42, 71, 142, 213, 426, 497, 994, 1491, 2982
The HCF of 2123,2982 is 1.
Lets's calculate GCF of 2123,2982
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2123,2982 By Matching Biggest Common Factor Method
Now, list down the factors of 2123
:1,11,193,2123
Now, list down the factors of 2982
:1,2,3,6,7,14,21,42,71,142,213,426,497,994,1491,2982
Greatest Common Factor
We found the factors 2123,2982 . The biggest common factor number is the GCF number.
So the greatest common factor 2123,2982 is 1.
Lets's calculate LCM of 756,728
| 2 | 756, 728 |
| 2 | 378, 364 |
| 7 | 189, 182 |
| 27, 26 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 27 x 26 = 19656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19656
Therefore, the GCF of Fractions 2123/756,2982/728 is 1/19656
Least Common Multiple of 756,728 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 756,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,728) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(756,728) x common factors =28 x 1 = 28
LCM(756,728) = ( 756 × 728 ) / 28
LCM(756,728) = 550368 / 28
LCM(756,728) = 19656
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FAQs on GCF of Fractions of 2123/756, 2982/728
1. What is the HCF of 2123,2982?
The HCF of 2123,2982 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 2123/756, 2982/728?
Answer: GCF of Numerators as per given numbers 2123/756, 2982/728 is
GCF of Numerators i.e. for 2123,2982 is 1
LCM of denominators i.e. for 756,728 is 19656.
Thus, GCF of Fractions is 1/19656.Finally, GCF of Fractions for 2123/756, 2982/728 is 1/19656.