GCF of 1953/458, 8400/4002
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1953/458, 8400/4002 i.e 21/916458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1953/458, 8400/4002.
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 1953/458,8400/4002?
Given fractions are 1953/458,8400/4002
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 1953/458,8400/4002, numerators are 1953,8400
Denominators are 458,4002
The GCF of 1953,8400 is 21 .
LCM of 458,4002 is 916458.
The greatest common factor of 1953/458,8400/4002 = [GCF of 1953,8400]/[LCM of 458,4002]= 21/916458
Therefore, the GCF of 1953/458,8400/4002 is 21/916458.
To find the highest common factor of 1953,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 1953 are 1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953
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 1953,8400 is 21.
Lets's calculate GCF of 1953,8400
| 3 | 1953, 8400 |
| 7 | 651, 2800 |
| 93, 400 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 1953,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 1953
:1,3,7,9,21,31,63,93,217,279,651,1953
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 1953,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 1953,8400 is 21.
Lets's calculate LCM of 458,4002
| 2 | 458, 4002 |
| 229, 2001 |
∴ So the LCM of the given numbers is 2 x 229 x 2001 = 916458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/916458
Therefore, the GCF of Fractions 1953/458,8400/4002 is 21/916458
Least Common Multiple of 458,4002 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 458,4002 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,4002) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(458,4002) x common factors =2 x 1 = 2
LCM(458,4002) = ( 458 × 4002 ) / 2
LCM(458,4002) = 1832916 / 2
LCM(458,4002) = 916458
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FAQs on GCF of Fractions of 1953/458, 8400/4002
1. What is the HCF of 1953,8400?
The HCF of 1953,8400 is 21
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 1953/458, 8400/4002?
Answer: GCF of Numerators as per given numbers 1953/458, 8400/4002 is
GCF of Numerators i.e. for 1953,8400 is 21
LCM of denominators i.e. for 458,4002 is 916458.
Thus, GCF of Fractions is 21/916458.Finally, GCF of Fractions for 1953/458, 8400/4002 is 21/916458.