GCF of 750/324, 5640/7782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 750/324, 5640/7782 i.e 30/420228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 750/324, 5640/7782.
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 750/324,5640/7782?
Given fractions are 750/324,5640/7782
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 750/324,5640/7782, numerators are 750,5640
Denominators are 324,7782
The GCF of 750,5640 is 30 .
LCM of 324,7782 is 420228.
The greatest common factor of 750/324,5640/7782 = [GCF of 750,5640]/[LCM of 324,7782]= 30/420228
Therefore, the GCF of 750/324,5640/7782 is 30/420228.
To find the highest common factor of 750,5640, we have to find the factors of both numbers and list the highest common factor.
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
The factors of 5640 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 47, 60, 94, 120, 141, 188, 235, 282, 376, 470, 564, 705, 940, 1128, 1410, 1880, 2820, 5640
The HCF of 750,5640 is 30.
Lets's calculate GCF of 750,5640
| 2 | 750, 5640 |
| 3 | 375, 2820 |
| 5 | 125, 940 |
| 25, 188 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 750,5640 By Matching Biggest Common Factor Method
Now, list down the factors of 750
:1,2,3,5,6,10,15,25,30,50,75,125,150,250,375,750
Now, list down the factors of 5640
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,47,60,94,120,141,188,235,282,376,470,564,705,940,1128,1410,1880,2820,5640
Greatest Common Factor
We found the factors 750,5640 . The biggest common factor number is the GCF number.
So the greatest common factor 750,5640 is 30.
Lets's calculate LCM of 324,7782
| 2 | 324, 7782 |
| 3 | 162, 3891 |
| 54, 1297 |
∴ So the LCM of the given numbers is 2 x 3 x 54 x 1297 = 420228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/420228
Therefore, the GCF of Fractions 750/324,5640/7782 is 30/420228
Least Common Multiple of 324,7782 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 324,7782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,7782) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(324,7782) x common factors =6 x 1 = 6
LCM(324,7782) = ( 324 × 7782 ) / 6
LCM(324,7782) = 2521368 / 6
LCM(324,7782) = 420228
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FAQs on GCF of Fractions of 750/324, 5640/7782
1. What is the HCF of 750,5640?
The HCF of 750,5640 is 30
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 750/324, 5640/7782?
Answer: GCF of Numerators as per given numbers 750/324, 5640/7782 is
GCF of Numerators i.e. for 750,5640 is 30
LCM of denominators i.e. for 324,7782 is 420228.
Thus, GCF of Fractions is 30/420228.Finally, GCF of Fractions for 750/324, 5640/7782 is 30/420228.