GCF of 2278/849, 1006/9744
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2278/849, 1006/9744 i.e 2/2757552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2278/849, 1006/9744.
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 2278/849,1006/9744?
Given fractions are 2278/849,1006/9744
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 2278/849,1006/9744, numerators are 2278,1006
Denominators are 849,9744
The GCF of 2278,1006 is 2 .
LCM of 849,9744 is 2757552.
The greatest common factor of 2278/849,1006/9744 = [GCF of 2278,1006]/[LCM of 849,9744]= 2/2757552
Therefore, the GCF of 2278/849,1006/9744 is 2/2757552.
To find the highest common factor of 2278,1006, we have to find the factors of both numbers and list the highest common factor.
The factors of 2278 are 1, 2, 17, 34, 67, 134, 1139, 2278
The factors of 1006 are 1, 2, 503, 1006
The HCF of 2278,1006 is 2.
Lets's calculate GCF of 2278,1006
| 2 | 2278, 1006 |
| 1139, 503 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2278,1006 By Matching Biggest Common Factor Method
Now, list down the factors of 2278
:1,2,17,34,67,134,1139,2278
Now, list down the factors of 1006
:1,2,503,1006
Greatest Common Factor
We found the factors 2278,1006 . The biggest common factor number is the GCF number.
So the greatest common factor 2278,1006 is 2.
Lets's calculate LCM of 849,9744
| 3 | 849, 9744 |
| 283, 3248 |
∴ So the LCM of the given numbers is 3 x 283 x 3248 = 2757552
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2757552
Therefore, the GCF of Fractions 2278/849,1006/9744 is 2/2757552
Least Common Multiple of 849,9744 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 849,9744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(849,9744) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(849,9744) x common factors =3 x 1 = 3
LCM(849,9744) = ( 849 × 9744 ) / 3
LCM(849,9744) = 8272656 / 3
LCM(849,9744) = 2757552
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FAQs on GCF of Fractions of 2278/849, 1006/9744
1. What is the HCF of 2278,1006?
The HCF of 2278,1006 is 2
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 2278/849, 1006/9744?
Answer: GCF of Numerators as per given numbers 2278/849, 1006/9744 is
GCF of Numerators i.e. for 2278,1006 is 2
LCM of denominators i.e. for 849,9744 is 2757552.
Thus, GCF of Fractions is 2/2757552.Finally, GCF of Fractions for 2278/849, 1006/9744 is 2/2757552.