GCF of 8040/279, 8176/7734
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8040/279, 8176/7734 i.e 8/719262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8040/279, 8176/7734.
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 8040/279,8176/7734?
Given fractions are 8040/279,8176/7734
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 8040/279,8176/7734, numerators are 8040,8176
Denominators are 279,7734
The GCF of 8040,8176 is 8 .
LCM of 279,7734 is 719262.
The greatest common factor of 8040/279,8176/7734 = [GCF of 8040,8176]/[LCM of 279,7734]= 8/719262
Therefore, the GCF of 8040/279,8176/7734 is 8/719262.
To find the highest common factor of 8040,8176, we have to find the factors of both numbers and list the highest common factor.
The factors of 8040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 67, 120, 134, 201, 268, 335, 402, 536, 670, 804, 1005, 1340, 1608, 2010, 2680, 4020, 8040
The factors of 8176 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 73, 112, 146, 292, 511, 584, 1022, 1168, 2044, 4088, 8176
The HCF of 8040,8176 is 8.
Lets's calculate GCF of 8040,8176
| 2 | 8040, 8176 |
| 2 | 4020, 4088 |
| 2 | 2010, 2044 |
| 1005, 1022 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 8040,8176 By Matching Biggest Common Factor Method
Now, list down the factors of 8040
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,67,120,134,201,268,335,402,536,670,804,1005,1340,1608,2010,2680,4020,8040
Now, list down the factors of 8176
:1,2,4,7,8,14,16,28,56,73,112,146,292,511,584,1022,1168,2044,4088,8176
Greatest Common Factor
We found the factors 8040,8176 . The biggest common factor number is the GCF number.
So the greatest common factor 8040,8176 is 8.
Lets's calculate LCM of 279,7734
| 3 | 279, 7734 |
| 93, 2578 |
∴ So the LCM of the given numbers is 3 x 93 x 2578 = 719262
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/719262
Therefore, the GCF of Fractions 8040/279,8176/7734 is 8/719262
Least Common Multiple of 279,7734 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 279,7734 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(279,7734) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(279,7734) x common factors =3 x 1 = 3
LCM(279,7734) = ( 279 × 7734 ) / 3
LCM(279,7734) = 2157786 / 3
LCM(279,7734) = 719262
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FAQs on GCF of Fractions of 8040/279, 8176/7734
1. What is the HCF of 8040,8176?
The HCF of 8040,8176 is 8
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 8040/279, 8176/7734?
Answer: GCF of Numerators as per given numbers 8040/279, 8176/7734 is
GCF of Numerators i.e. for 8040,8176 is 8
LCM of denominators i.e. for 279,7734 is 719262.
Thus, GCF of Fractions is 8/719262.Finally, GCF of Fractions for 8040/279, 8176/7734 is 8/719262.