GCF of 8400/279, 4310/3968
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8400/279, 4310/3968 i.e 10/35712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8400/279, 4310/3968.
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 8400/279,4310/3968?
Given fractions are 8400/279,4310/3968
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 8400/279,4310/3968, numerators are 8400,4310
Denominators are 279,3968
The GCF of 8400,4310 is 10 .
LCM of 279,3968 is 35712.
The greatest common factor of 8400/279,4310/3968 = [GCF of 8400,4310]/[LCM of 279,3968]= 10/35712
Therefore, the GCF of 8400/279,4310/3968 is 10/35712.
To find the highest common factor of 8400,4310, we have to find the factors of both numbers and list the highest common factor.
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 factors of 4310 are 1, 2, 5, 10, 431, 862, 2155, 4310
The HCF of 8400,4310 is 10.
Lets's calculate GCF of 8400,4310
| 2 | 8400, 4310 |
| 5 | 4200, 2155 |
| 840, 431 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 8400,4310 By Matching Biggest Common Factor Method
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
Now, list down the factors of 4310
:1,2,5,10,431,862,2155,4310
Greatest Common Factor
We found the factors 8400,4310 . The biggest common factor number is the GCF number.
So the greatest common factor 8400,4310 is 10.
Lets's calculate LCM of 279,3968
| 31 | 279, 3968 |
| 9, 128 |
∴ So the LCM of the given numbers is 31 x 9 x 128 = 35712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/35712
Therefore, the GCF of Fractions 8400/279,4310/3968 is 10/35712
Least Common Multiple of 279,3968 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 279,3968 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(279,3968) = 31
common factors(in case of two or more numbers have common factors) = 1
GCF(279,3968) x common factors =31 x 1 = 31
LCM(279,3968) = ( 279 × 3968 ) / 31
LCM(279,3968) = 1107072 / 31
LCM(279,3968) = 35712
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FAQs on GCF of Fractions of 8400/279, 4310/3968
1. What is the HCF of 8400,4310?
The HCF of 8400,4310 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 8400/279, 4310/3968?
Answer: GCF of Numerators as per given numbers 8400/279, 4310/3968 is
GCF of Numerators i.e. for 8400,4310 is 10
LCM of denominators i.e. for 279,3968 is 35712.
Thus, GCF of Fractions is 10/35712.Finally, GCF of Fractions for 8400/279, 4310/3968 is 10/35712.