GCF of 5695/256, 8400/7302
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5695/256, 8400/7302 i.e 5/934656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5695/256, 8400/7302.
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 5695/256,8400/7302?
Given fractions are 5695/256,8400/7302
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 5695/256,8400/7302, numerators are 5695,8400
Denominators are 256,7302
The GCF of 5695,8400 is 5 .
LCM of 256,7302 is 934656.
The greatest common factor of 5695/256,8400/7302 = [GCF of 5695,8400]/[LCM of 256,7302]= 5/934656
Therefore, the GCF of 5695/256,8400/7302 is 5/934656.
To find the highest common factor of 5695,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 5695 are 1, 5, 17, 67, 85, 335, 1139, 5695
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 5695,8400 is 5.
Lets's calculate GCF of 5695,8400
| 5 | 5695, 8400 |
| 1139, 1680 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 5695,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 5695
:1,5,17,67,85,335,1139,5695
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 5695,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 5695,8400 is 5.
Lets's calculate LCM of 256,7302
| 2 | 256, 7302 |
| 128, 3651 |
∴ So the LCM of the given numbers is 2 x 128 x 3651 = 934656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/934656
Therefore, the GCF of Fractions 5695/256,8400/7302 is 5/934656
Least Common Multiple of 256,7302 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 256,7302 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(256,7302) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(256,7302) x common factors =2 x 1 = 2
LCM(256,7302) = ( 256 × 7302 ) / 2
LCM(256,7302) = 1869312 / 2
LCM(256,7302) = 934656
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FAQs on GCF of Fractions of 5695/256, 8400/7302
1. What is the HCF of 5695,8400?
The HCF of 5695,8400 is 5
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 5695/256, 8400/7302?
Answer: GCF of Numerators as per given numbers 5695/256, 8400/7302 is
GCF of Numerators i.e. for 5695,8400 is 5
LCM of denominators i.e. for 256,7302 is 934656.
Thus, GCF of Fractions is 5/934656.Finally, GCF of Fractions for 5695/256, 8400/7302 is 5/934656.