GCF of 2618/106, 8064/374
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2618/106, 8064/374 i.e 14/19822 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2618/106, 8064/374.
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 2618/106,8064/374?
Given fractions are 2618/106,8064/374
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 2618/106,8064/374, numerators are 2618,8064
Denominators are 106,374
The GCF of 2618,8064 is 14 .
LCM of 106,374 is 19822.
The greatest common factor of 2618/106,8064/374 = [GCF of 2618,8064]/[LCM of 106,374]= 14/19822
Therefore, the GCF of 2618/106,8064/374 is 14/19822.
To find the highest common factor of 2618,8064, we have to find the factors of both numbers and list the highest common factor.
The factors of 2618 are 1, 2, 7, 11, 14, 17, 22, 34, 77, 119, 154, 187, 238, 374, 1309, 2618
The factors of 8064 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 384, 448, 504, 576, 672, 896, 1008, 1152, 1344, 2016, 2688, 4032, 8064
The HCF of 2618,8064 is 14.
Lets's calculate GCF of 2618,8064
| 2 | 2618, 8064 |
| 7 | 1309, 4032 |
| 187, 576 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 2618,8064 By Matching Biggest Common Factor Method
Now, list down the factors of 2618
:1,2,7,11,14,17,22,34,77,119,154,187,238,374,1309,2618
Now, list down the factors of 8064
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,32,36,42,48,56,63,64,72,84,96,112,126,128,144,168,192,224,252,288,336,384,448,504,576,672,896,1008,1152,1344,2016,2688,4032,8064
Greatest Common Factor
We found the factors 2618,8064 . The biggest common factor number is the GCF number.
So the greatest common factor 2618,8064 is 14.
Lets's calculate LCM of 106,374
| 2 | 106, 374 |
| 53, 187 |
∴ So the LCM of the given numbers is 2 x 53 x 187 = 19822
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/19822
Therefore, the GCF of Fractions 2618/106,8064/374 is 14/19822
Least Common Multiple of 106,374 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 106,374 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,374) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,374) x common factors =2 x 1 = 2
LCM(106,374) = ( 106 × 374 ) / 2
LCM(106,374) = 39644 / 2
LCM(106,374) = 19822
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FAQs on GCF of Fractions of 2618/106, 8064/374
1. What is the HCF of 2618,8064?
The HCF of 2618,8064 is 14
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 2618/106, 8064/374?
Answer: GCF of Numerators as per given numbers 2618/106, 8064/374 is
GCF of Numerators i.e. for 2618,8064 is 14
LCM of denominators i.e. for 106,374 is 19822.
Thus, GCF of Fractions is 14/19822.Finally, GCF of Fractions for 2618/106, 8064/374 is 14/19822.