GCF of 903/416, 840/904
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 903/416, 840/904 i.e 21/47008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 903/416, 840/904.
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 903/416,840/904?
Given fractions are 903/416,840/904
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 903/416,840/904, numerators are 903,840
Denominators are 416,904
The GCF of 903,840 is 21 .
LCM of 416,904 is 47008.
The greatest common factor of 903/416,840/904 = [GCF of 903,840]/[LCM of 416,904]= 21/47008
Therefore, the GCF of 903/416,840/904 is 21/47008.
To find the highest common factor of 903,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 903 are 1, 3, 7, 21, 43, 129, 301, 903
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 903,840 is 21.
Lets's calculate GCF of 903,840
| 3 | 903, 840 |
| 7 | 301, 280 |
| 43, 40 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 903,840 By Matching Biggest Common Factor Method
Now, list down the factors of 903
:1,3,7,21,43,129,301,903
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 903,840 . The biggest common factor number is the GCF number.
So the greatest common factor 903,840 is 21.
Lets's calculate LCM of 416,904
| 2 | 416, 904 |
| 2 | 208, 452 |
| 2 | 104, 226 |
| 52, 113 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 52 x 113 = 47008
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/47008
Therefore, the GCF of Fractions 903/416,840/904 is 21/47008
Least Common Multiple of 416,904 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 416,904 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,904) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(416,904) x common factors =8 x 1 = 8
LCM(416,904) = ( 416 × 904 ) / 8
LCM(416,904) = 376064 / 8
LCM(416,904) = 47008
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FAQs on GCF of Fractions of 903/416, 840/904
1. What is the HCF of 903,840?
The HCF of 903,840 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 903/416, 840/904?
Answer: GCF of Numerators as per given numbers 903/416, 840/904 is
GCF of Numerators i.e. for 903,840 is 21
LCM of denominators i.e. for 416,904 is 47008.
Thus, GCF of Fractions is 21/47008.Finally, GCF of Fractions for 903/416, 840/904 is 21/47008.