GCF of 3000/828, 4080/158
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3000/828, 4080/158 i.e 120/65412 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3000/828, 4080/158.
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 3000/828,4080/158?
Given fractions are 3000/828,4080/158
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 3000/828,4080/158, numerators are 3000,4080
Denominators are 828,158
The GCF of 3000,4080 is 120 .
LCM of 828,158 is 65412.
The greatest common factor of 3000/828,4080/158 = [GCF of 3000,4080]/[LCM of 828,158]= 120/65412
Therefore, the GCF of 3000/828,4080/158 is 120/65412.
To find the highest common factor of 3000,4080, we have to find the factors of both numbers and list the highest common factor.
The factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000
The factors of 4080 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 34, 40, 48, 51, 60, 68, 80, 85, 102, 120, 136, 170, 204, 240, 255, 272, 340, 408, 510, 680, 816, 1020, 1360, 2040, 4080
The HCF of 3000,4080 is 120.
Lets's calculate GCF of 3000,4080
| 2 | 3000, 4080 |
| 2 | 1500, 2040 |
| 2 | 750, 1020 |
| 3 | 375, 510 |
| 5 | 125, 170 |
| 25, 34 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 5 = 120
Greatest Common Factor of 3000,4080 By Matching Biggest Common Factor Method
Now, list down the factors of 3000
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000
Now, list down the factors of 4080
:1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,34,40,48,51,60,68,80,85,102,120,136,170,204,240,255,272,340,408,510,680,816,1020,1360,2040,4080
Greatest Common Factor
We found the factors 3000,4080 . The biggest common factor number is the GCF number.
So the greatest common factor 3000,4080 is 120.
Lets's calculate LCM of 828,158
| 2 | 828, 158 |
| 414, 79 |
∴ So the LCM of the given numbers is 2 x 414 x 79 = 65412
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 120/65412
Therefore, the GCF of Fractions 3000/828,4080/158 is 120/65412
Least Common Multiple of 828,158 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 828,158 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,158) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(828,158) x common factors =2 x 1 = 2
LCM(828,158) = ( 828 × 158 ) / 2
LCM(828,158) = 130824 / 2
LCM(828,158) = 65412
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FAQs on GCF of Fractions of 3000/828, 4080/158
1. What is the HCF of 3000,4080?
The HCF of 3000,4080 is 120
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 3000/828, 4080/158?
Answer: GCF of Numerators as per given numbers 3000/828, 4080/158 is
GCF of Numerators i.e. for 3000,4080 is 120
LCM of denominators i.e. for 828,158 is 65412.
Thus, GCF of Fractions is 120/65412.Finally, GCF of Fractions for 3000/828, 4080/158 is 120/65412.