GCF of 2400/334, 7812/8370
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2400/334, 7812/8370 i.e 12/1397790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2400/334, 7812/8370.
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 2400/334,7812/8370?
Given fractions are 2400/334,7812/8370
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 2400/334,7812/8370, numerators are 2400,7812
Denominators are 334,8370
The GCF of 2400,7812 is 12 .
LCM of 334,8370 is 1397790.
The greatest common factor of 2400/334,7812/8370 = [GCF of 2400,7812]/[LCM of 334,8370]= 12/1397790
Therefore, the GCF of 2400/334,7812/8370 is 12/1397790.
To find the highest common factor of 2400,7812, we have to find the factors of both numbers and list the highest common factor.
The factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400
The factors of 7812 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 31, 36, 42, 62, 63, 84, 93, 124, 126, 186, 217, 252, 279, 372, 434, 558, 651, 868, 1116, 1302, 1953, 2604, 3906, 7812
The HCF of 2400,7812 is 12.
Lets's calculate GCF of 2400,7812
| 2 | 2400, 7812 |
| 2 | 1200, 3906 |
| 3 | 600, 1953 |
| 200, 651 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 2400,7812 By Matching Biggest Common Factor Method
Now, list down the factors of 2400
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,32,40,48,50,60,75,80,96,100,120,150,160,200,240,300,400,480,600,800,1200,2400
Now, list down the factors of 7812
:1,2,3,4,6,7,9,12,14,18,21,28,31,36,42,62,63,84,93,124,126,186,217,252,279,372,434,558,651,868,1116,1302,1953,2604,3906,7812
Greatest Common Factor
We found the factors 2400,7812 . The biggest common factor number is the GCF number.
So the greatest common factor 2400,7812 is 12.
Lets's calculate LCM of 334,8370
| 2 | 334, 8370 |
| 167, 4185 |
∴ So the LCM of the given numbers is 2 x 167 x 4185 = 1397790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/1397790
Therefore, the GCF of Fractions 2400/334,7812/8370 is 12/1397790
Least Common Multiple of 334,8370 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 334,8370 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(334,8370) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(334,8370) x common factors =2 x 1 = 2
LCM(334,8370) = ( 334 × 8370 ) / 2
LCM(334,8370) = 2795580 / 2
LCM(334,8370) = 1397790
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FAQs on GCF of Fractions of 2400/334, 7812/8370
1. What is the HCF of 2400,7812?
The HCF of 2400,7812 is 12
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 2400/334, 7812/8370?
Answer: GCF of Numerators as per given numbers 2400/334, 7812/8370 is
GCF of Numerators i.e. for 2400,7812 is 12
LCM of denominators i.e. for 334,8370 is 1397790.
Thus, GCF of Fractions is 12/1397790.Finally, GCF of Fractions for 2400/334, 7812/8370 is 12/1397790.