GCF of 8112/414, 3360/2478
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8112/414, 3360/2478 i.e 48/170982 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8112/414, 3360/2478.
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 8112/414,3360/2478?
Given fractions are 8112/414,3360/2478
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 8112/414,3360/2478, numerators are 8112,3360
Denominators are 414,2478
The GCF of 8112,3360 is 48 .
LCM of 414,2478 is 170982.
The greatest common factor of 8112/414,3360/2478 = [GCF of 8112,3360]/[LCM of 414,2478]= 48/170982
Therefore, the GCF of 8112/414,3360/2478 is 48/170982.
To find the highest common factor of 8112,3360, we have to find the factors of both numbers and list the highest common factor.
The factors of 8112 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 169, 208, 312, 338, 507, 624, 676, 1014, 1352, 2028, 2704, 4056, 8112
The factors of 3360 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1120, 1680, 3360
The HCF of 8112,3360 is 48.
Lets's calculate GCF of 8112,3360
| 2 | 8112, 3360 |
| 2 | 4056, 1680 |
| 2 | 2028, 840 |
| 2 | 1014, 420 |
| 3 | 507, 210 |
| 169, 70 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Greatest Common Factor of 8112,3360 By Matching Biggest Common Factor Method
Now, list down the factors of 8112
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,169,208,312,338,507,624,676,1014,1352,2028,2704,4056,8112
Now, list down the factors of 3360
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,32,35,40,42,48,56,60,70,80,84,96,105,112,120,140,160,168,210,224,240,280,336,420,480,560,672,840,1120,1680,3360
Greatest Common Factor
We found the factors 8112,3360 . The biggest common factor number is the GCF number.
So the greatest common factor 8112,3360 is 48.
Lets's calculate LCM of 414,2478
| 2 | 414, 2478 |
| 3 | 207, 1239 |
| 69, 413 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 413 = 170982
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/170982
Therefore, the GCF of Fractions 8112/414,3360/2478 is 48/170982
Least Common Multiple of 414,2478 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 414,2478 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,2478) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,2478) x common factors =6 x 1 = 6
LCM(414,2478) = ( 414 × 2478 ) / 6
LCM(414,2478) = 1025892 / 6
LCM(414,2478) = 170982
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FAQs on GCF of Fractions of 8112/414, 3360/2478
1. What is the HCF of 8112,3360?
The HCF of 8112,3360 is 48
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 8112/414, 3360/2478?
Answer: GCF of Numerators as per given numbers 8112/414, 3360/2478 is
GCF of Numerators i.e. for 8112,3360 is 48
LCM of denominators i.e. for 414,2478 is 170982.
Thus, GCF of Fractions is 48/170982.Finally, GCF of Fractions for 8112/414, 3360/2478 is 48/170982.