GCF of 4200/864, 6566/9582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4200/864, 6566/9582 i.e 14/1379808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4200/864, 6566/9582.
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 4200/864,6566/9582?
Given fractions are 4200/864,6566/9582
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 4200/864,6566/9582, numerators are 4200,6566
Denominators are 864,9582
The GCF of 4200,6566 is 14 .
LCM of 864,9582 is 1379808.
The greatest common factor of 4200/864,6566/9582 = [GCF of 4200,6566]/[LCM of 864,9582]= 14/1379808
Therefore, the GCF of 4200/864,6566/9582 is 14/1379808.
To find the highest common factor of 4200,6566, we have to find the factors of both numbers and list the highest common factor.
The factors of 4200 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200
The factors of 6566 are 1, 2, 7, 14, 49, 67, 98, 134, 469, 938, 3283, 6566
The HCF of 4200,6566 is 14.
Lets's calculate GCF of 4200,6566
| 2 | 4200, 6566 |
| 7 | 2100, 3283 |
| 300, 469 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 4200,6566 By Matching Biggest Common Factor Method
Now, list down the factors of 4200
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,25,28,30,35,40,42,50,56,60,70,75,84,100,105,120,140,150,168,175,200,210,280,300,350,420,525,600,700,840,1050,1400,2100,4200
Now, list down the factors of 6566
:1,2,7,14,49,67,98,134,469,938,3283,6566
Greatest Common Factor
We found the factors 4200,6566 . The biggest common factor number is the GCF number.
So the greatest common factor 4200,6566 is 14.
Lets's calculate LCM of 864,9582
| 2 | 864, 9582 |
| 3 | 432, 4791 |
| 144, 1597 |
∴ So the LCM of the given numbers is 2 x 3 x 144 x 1597 = 1379808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1379808
Therefore, the GCF of Fractions 4200/864,6566/9582 is 14/1379808
Least Common Multiple of 864,9582 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 864,9582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(864,9582) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(864,9582) x common factors =6 x 1 = 6
LCM(864,9582) = ( 864 × 9582 ) / 6
LCM(864,9582) = 8278848 / 6
LCM(864,9582) = 1379808
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 4200/864, 6566/9582
1. What is the HCF of 4200,6566?
The HCF of 4200,6566 is 14
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 4200/864, 6566/9582?
Answer: GCF of Numerators as per given numbers 4200/864, 6566/9582 is
GCF of Numerators i.e. for 4200,6566 is 14
LCM of denominators i.e. for 864,9582 is 1379808.
Thus, GCF of Fractions is 14/1379808.Finally, GCF of Fractions for 4200/864, 6566/9582 is 14/1379808.