GCF of 7749/840, 1648/9688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7749/840, 1648/9688 i.e 1/145320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7749/840, 1648/9688.
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 7749/840,1648/9688?
Given fractions are 7749/840,1648/9688
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 7749/840,1648/9688, numerators are 7749,1648
Denominators are 840,9688
The GCF of 7749,1648 is 1 .
LCM of 840,9688 is 145320.
The greatest common factor of 7749/840,1648/9688 = [GCF of 7749,1648]/[LCM of 840,9688]= 1/145320
Therefore, the GCF of 7749/840,1648/9688 is 1/145320.
To find the highest common factor of 7749,1648, we have to find the factors of both numbers and list the highest common factor.
The factors of 7749 are 1, 3, 7, 9, 21, 27, 41, 63, 123, 189, 287, 369, 861, 1107, 2583, 7749
The factors of 1648 are 1, 2, 4, 8, 16, 103, 206, 412, 824, 1648
The HCF of 7749,1648 is 1.
Lets's calculate GCF of 7749,1648
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7749,1648 By Matching Biggest Common Factor Method
Now, list down the factors of 7749
:1,3,7,9,21,27,41,63,123,189,287,369,861,1107,2583,7749
Now, list down the factors of 1648
:1,2,4,8,16,103,206,412,824,1648
Greatest Common Factor
We found the factors 7749,1648 . The biggest common factor number is the GCF number.
So the greatest common factor 7749,1648 is 1.
Lets's calculate LCM of 840,9688
| 2 | 840, 9688 |
| 2 | 420, 4844 |
| 2 | 210, 2422 |
| 7 | 105, 1211 |
| 15, 173 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 15 x 173 = 145320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/145320
Therefore, the GCF of Fractions 7749/840,1648/9688 is 1/145320
Least Common Multiple of 840,9688 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 840,9688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,9688) = 56
common factors(in case of two or more numbers have common factors) = 1
GCF(840,9688) x common factors =56 x 1 = 56
LCM(840,9688) = ( 840 × 9688 ) / 56
LCM(840,9688) = 8137920 / 56
LCM(840,9688) = 145320
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7749/840, 1648/9688
1. What is the HCF of 7749,1648?
The HCF of 7749,1648 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 7749/840, 1648/9688?
Answer: GCF of Numerators as per given numbers 7749/840, 1648/9688 is
GCF of Numerators i.e. for 7749,1648 is 1
LCM of denominators i.e. for 840,9688 is 145320.
Thus, GCF of Fractions is 1/145320.Finally, GCF of Fractions for 7749/840, 1648/9688 is 1/145320.