GCF of 8424/396, 7138/1896
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8424/396, 7138/1896 i.e 2/62568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8424/396, 7138/1896.
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 8424/396,7138/1896?
Given fractions are 8424/396,7138/1896
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 8424/396,7138/1896, numerators are 8424,7138
Denominators are 396,1896
The GCF of 8424,7138 is 2 .
LCM of 396,1896 is 62568.
The greatest common factor of 8424/396,7138/1896 = [GCF of 8424,7138]/[LCM of 396,1896]= 2/62568
Therefore, the GCF of 8424/396,7138/1896 is 2/62568.
To find the highest common factor of 8424,7138, we have to find the factors of both numbers and list the highest common factor.
The factors of 8424 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 81, 104, 108, 117, 156, 162, 216, 234, 312, 324, 351, 468, 648, 702, 936, 1053, 1404, 2106, 2808, 4212, 8424
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The HCF of 8424,7138 is 2.
Lets's calculate GCF of 8424,7138
| 2 | 8424, 7138 |
| 4212, 3569 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8424,7138 By Matching Biggest Common Factor Method
Now, list down the factors of 8424
:1,2,3,4,6,8,9,12,13,18,24,26,27,36,39,52,54,72,78,81,104,108,117,156,162,216,234,312,324,351,468,648,702,936,1053,1404,2106,2808,4212,8424
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Greatest Common Factor
We found the factors 8424,7138 . The biggest common factor number is the GCF number.
So the greatest common factor 8424,7138 is 2.
Lets's calculate LCM of 396,1896
| 2 | 396, 1896 |
| 2 | 198, 948 |
| 3 | 99, 474 |
| 33, 158 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 33 x 158 = 62568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/62568
Therefore, the GCF of Fractions 8424/396,7138/1896 is 2/62568
Least Common Multiple of 396,1896 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 396,1896 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(396,1896) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(396,1896) x common factors =12 x 1 = 12
LCM(396,1896) = ( 396 × 1896 ) / 12
LCM(396,1896) = 750816 / 12
LCM(396,1896) = 62568
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FAQs on GCF of Fractions of 8424/396, 7138/1896
1. What is the HCF of 8424,7138?
The HCF of 8424,7138 is 2
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 8424/396, 7138/1896?
Answer: GCF of Numerators as per given numbers 8424/396, 7138/1896 is
GCF of Numerators i.e. for 8424,7138 is 2
LCM of denominators i.e. for 396,1896 is 62568.
Thus, GCF of Fractions is 2/62568.Finally, GCF of Fractions for 8424/396, 7138/1896 is 2/62568.