GCF of 7614/528, 1746/2720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7614/528, 1746/2720 i.e 18/89760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7614/528, 1746/2720.
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 7614/528,1746/2720?
Given fractions are 7614/528,1746/2720
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 7614/528,1746/2720, numerators are 7614,1746
Denominators are 528,2720
The GCF of 7614,1746 is 18 .
LCM of 528,2720 is 89760.
The greatest common factor of 7614/528,1746/2720 = [GCF of 7614,1746]/[LCM of 528,2720]= 18/89760
Therefore, the GCF of 7614/528,1746/2720 is 18/89760.
To find the highest common factor of 7614,1746, we have to find the factors of both numbers and list the highest common factor.
The factors of 7614 are 1, 2, 3, 6, 9, 18, 27, 47, 54, 81, 94, 141, 162, 282, 423, 846, 1269, 2538, 3807, 7614
The factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746
The HCF of 7614,1746 is 18.
Lets's calculate GCF of 7614,1746
| 2 | 7614, 1746 |
| 3 | 3807, 873 |
| 3 | 1269, 291 |
| 423, 97 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 7614,1746 By Matching Biggest Common Factor Method
Now, list down the factors of 7614
:1,2,3,6,9,18,27,47,54,81,94,141,162,282,423,846,1269,2538,3807,7614
Now, list down the factors of 1746
:1,2,3,6,9,18,97,194,291,582,873,1746
Greatest Common Factor
We found the factors 7614,1746 . The biggest common factor number is the GCF number.
So the greatest common factor 7614,1746 is 18.
Lets's calculate LCM of 528,2720
| 2 | 528, 2720 |
| 2 | 264, 1360 |
| 2 | 132, 680 |
| 2 | 66, 340 |
| 33, 170 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 33 x 170 = 89760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/89760
Therefore, the GCF of Fractions 7614/528,1746/2720 is 18/89760
Least Common Multiple of 528,2720 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 528,2720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(528,2720) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(528,2720) x common factors =16 x 1 = 16
LCM(528,2720) = ( 528 × 2720 ) / 16
LCM(528,2720) = 1436160 / 16
LCM(528,2720) = 89760
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FAQs on GCF of Fractions of 7614/528, 1746/2720
1. What is the HCF of 7614,1746?
The HCF of 7614,1746 is 18
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 7614/528, 1746/2720?
Answer: GCF of Numerators as per given numbers 7614/528, 1746/2720 is
GCF of Numerators i.e. for 7614,1746 is 18
LCM of denominators i.e. for 528,2720 is 89760.
Thus, GCF of Fractions is 18/89760.Finally, GCF of Fractions for 7614/528, 1746/2720 is 18/89760.