GCF of 8290/138, 8400/7793
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8290/138, 8400/7793 i.e 10/1075434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8290/138, 8400/7793.
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 8290/138,8400/7793?
Given fractions are 8290/138,8400/7793
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 8290/138,8400/7793, numerators are 8290,8400
Denominators are 138,7793
The GCF of 8290,8400 is 10 .
LCM of 138,7793 is 1075434.
The greatest common factor of 8290/138,8400/7793 = [GCF of 8290,8400]/[LCM of 138,7793]= 10/1075434
Therefore, the GCF of 8290/138,8400/7793 is 10/1075434.
To find the highest common factor of 8290,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 8290 are 1, 2, 5, 10, 829, 1658, 4145, 8290
The factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400
The HCF of 8290,8400 is 10.
Lets's calculate GCF of 8290,8400
| 2 | 8290, 8400 |
| 5 | 4145, 4200 |
| 829, 840 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 8290,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 8290
:1,2,5,10,829,1658,4145,8290
Now, list down the factors of 8400
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,25,28,30,35,40,42,48,50,56,60,70,75,80,84,100,105,112,120,140,150,168,175,200,210,240,280,300,336,350,400,420,525,560,600,700,840,1050,1200,1400,1680,2100,2800,4200,8400
Greatest Common Factor
We found the factors 8290,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 8290,8400 is 10.
Lets's calculate LCM of 138,7793
Given numbers has no common factors except 1. So, there LCM is their product i.e 1075434
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1075434
Therefore, the GCF of Fractions 8290/138,8400/7793 is 10/1075434
Least Common Multiple of 138,7793 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 138,7793 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(138,7793) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(138,7793) x common factors =1 x 1 = 1
LCM(138,7793) = ( 138 × 7793 ) / 1
LCM(138,7793) = 1075434 / 1
LCM(138,7793) = 1075434
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FAQs on GCF of Fractions of 8290/138, 8400/7793
1. What is the HCF of 8290,8400?
The HCF of 8290,8400 is 10
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 8290/138, 8400/7793?
Answer: GCF of Numerators as per given numbers 8290/138, 8400/7793 is
GCF of Numerators i.e. for 8290,8400 is 10
LCM of denominators i.e. for 138,7793 is 1075434.
Thus, GCF of Fractions is 10/1075434.Finally, GCF of Fractions for 8290/138, 8400/7793 is 10/1075434.