GCF of 3408/783, 4200/3607
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3408/783, 4200/3607 i.e 24/2824281 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3408/783, 4200/3607.
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 3408/783,4200/3607?
Given fractions are 3408/783,4200/3607
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 3408/783,4200/3607, numerators are 3408,4200
Denominators are 783,3607
The GCF of 3408,4200 is 24 .
LCM of 783,3607 is 2824281.
The greatest common factor of 3408/783,4200/3607 = [GCF of 3408,4200]/[LCM of 783,3607]= 24/2824281
Therefore, the GCF of 3408/783,4200/3607 is 24/2824281.
To find the highest common factor of 3408,4200, we have to find the factors of both numbers and list the highest common factor.
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 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 HCF of 3408,4200 is 24.
Lets's calculate GCF of 3408,4200
| 2 | 3408, 4200 |
| 2 | 1704, 2100 |
| 2 | 852, 1050 |
| 3 | 426, 525 |
| 142, 175 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 3408,4200 By Matching Biggest Common Factor Method
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
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
Greatest Common Factor
We found the factors 3408,4200 . The biggest common factor number is the GCF number.
So the greatest common factor 3408,4200 is 24.
Lets's calculate LCM of 783,3607
Given numbers has no common factors except 1. So, there LCM is their product i.e 2824281
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/2824281
Therefore, the GCF of Fractions 3408/783,4200/3607 is 24/2824281
Least Common Multiple of 783,3607 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 783,3607 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(783,3607) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(783,3607) x common factors =1 x 1 = 1
LCM(783,3607) = ( 783 × 3607 ) / 1
LCM(783,3607) = 2824281 / 1
LCM(783,3607) = 2824281
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FAQs on GCF of Fractions of 3408/783, 4200/3607
1. What is the HCF of 3408,4200?
The HCF of 3408,4200 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 3408/783, 4200/3607?
Answer: GCF of Numerators as per given numbers 3408/783, 4200/3607 is
GCF of Numerators i.e. for 3408,4200 is 24
LCM of denominators i.e. for 783,3607 is 2824281.
Thus, GCF of Fractions is 24/2824281.Finally, GCF of Fractions for 3408/783, 4200/3607 is 24/2824281.