GCF of 4200/344, 3408/229
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4200/344, 3408/229 i.e 24/78776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4200/344, 3408/229.
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 4200/344,3408/229?
Given fractions are 4200/344,3408/229
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 4200/344,3408/229, numerators are 4200,3408
Denominators are 344,229
The GCF of 4200,3408 is 24 .
LCM of 344,229 is 78776.
The greatest common factor of 4200/344,3408/229 = [GCF of 4200,3408]/[LCM of 344,229]= 24/78776
Therefore, the GCF of 4200/344,3408/229 is 24/78776.
To find the highest common factor of 4200,3408, 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 3408 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 71, 142, 213, 284, 426, 568, 852, 1136, 1704, 3408
The HCF of 4200,3408 is 24.
Lets's calculate GCF of 4200,3408
| 2 | 4200, 3408 |
| 2 | 2100, 1704 |
| 2 | 1050, 852 |
| 3 | 525, 426 |
| 175, 142 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 4200,3408 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 3408
:1,2,3,4,6,8,12,16,24,48,71,142,213,284,426,568,852,1136,1704,3408
Greatest Common Factor
We found the factors 4200,3408 . The biggest common factor number is the GCF number.
So the greatest common factor 4200,3408 is 24.
Lets's calculate LCM of 344,229
Given numbers has no common factors except 1. So, there LCM is their product i.e 78776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/78776
Therefore, the GCF of Fractions 4200/344,3408/229 is 24/78776
Least Common Multiple of 344,229 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 344,229 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,229) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(344,229) x common factors =1 x 1 = 1
LCM(344,229) = ( 344 × 229 ) / 1
LCM(344,229) = 78776 / 1
LCM(344,229) = 78776
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 4200/344, 3408/229
1. What is the HCF of 4200,3408?
The HCF of 4200,3408 is 24
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 4200/344, 3408/229?
Answer: GCF of Numerators as per given numbers 4200/344, 3408/229 is
GCF of Numerators i.e. for 4200,3408 is 24
LCM of denominators i.e. for 344,229 is 78776.
Thus, GCF of Fractions is 24/78776.Finally, GCF of Fractions for 4200/344, 3408/229 is 24/78776.