GCF of 8358/110, 7728/262
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8358/110, 7728/262 i.e 42/14410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8358/110, 7728/262.
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 8358/110,7728/262?
Given fractions are 8358/110,7728/262
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 8358/110,7728/262, numerators are 8358,7728
Denominators are 110,262
The GCF of 8358,7728 is 42 .
LCM of 110,262 is 14410.
The greatest common factor of 8358/110,7728/262 = [GCF of 8358,7728]/[LCM of 110,262]= 42/14410
Therefore, the GCF of 8358/110,7728/262 is 42/14410.
To find the highest common factor of 8358,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 8358 are 1, 2, 3, 6, 7, 14, 21, 42, 199, 398, 597, 1194, 1393, 2786, 4179, 8358
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The HCF of 8358,7728 is 42.
Lets's calculate GCF of 8358,7728
| 2 | 8358, 7728 |
| 3 | 4179, 3864 |
| 7 | 1393, 1288 |
| 199, 184 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 8358,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 8358
:1,2,3,6,7,14,21,42,199,398,597,1194,1393,2786,4179,8358
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Greatest Common Factor
We found the factors 8358,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 8358,7728 is 42.
Lets's calculate LCM of 110,262
| 2 | 110, 262 |
| 55, 131 |
∴ So the LCM of the given numbers is 2 x 55 x 131 = 14410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/14410
Therefore, the GCF of Fractions 8358/110,7728/262 is 42/14410
Least Common Multiple of 110,262 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 110,262 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(110,262) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(110,262) x common factors =2 x 1 = 2
LCM(110,262) = ( 110 × 262 ) / 2
LCM(110,262) = 28820 / 2
LCM(110,262) = 14410
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FAQs on GCF of Fractions of 8358/110, 7728/262
1. What is the HCF of 8358,7728?
The HCF of 8358,7728 is 42
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 8358/110, 7728/262?
Answer: GCF of Numerators as per given numbers 8358/110, 7728/262 is
GCF of Numerators i.e. for 8358,7728 is 42
LCM of denominators i.e. for 110,262 is 14410.
Thus, GCF of Fractions is 42/14410.Finally, GCF of Fractions for 8358/110, 7728/262 is 42/14410.