GCF of 748/305, 4080/7046
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 748/305, 4080/7046 i.e 68/2149030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 748/305, 4080/7046.
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 748/305,4080/7046?
Given fractions are 748/305,4080/7046
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 748/305,4080/7046, numerators are 748,4080
Denominators are 305,7046
The GCF of 748,4080 is 68 .
LCM of 305,7046 is 2149030.
The greatest common factor of 748/305,4080/7046 = [GCF of 748,4080]/[LCM of 305,7046]= 68/2149030
Therefore, the GCF of 748/305,4080/7046 is 68/2149030.
To find the highest common factor of 748,4080, we have to find the factors of both numbers and list the highest common factor.
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The factors of 4080 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 34, 40, 48, 51, 60, 68, 80, 85, 102, 120, 136, 170, 204, 240, 255, 272, 340, 408, 510, 680, 816, 1020, 1360, 2040, 4080
The HCF of 748,4080 is 68.
Lets's calculate GCF of 748,4080
| 2 | 748, 4080 |
| 2 | 374, 2040 |
| 17 | 187, 1020 |
| 11, 60 |
∴ So the GCF of the given numbers is 2 x 2 x 17 = 68
Greatest Common Factor of 748,4080 By Matching Biggest Common Factor Method
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Now, list down the factors of 4080
:1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,34,40,48,51,60,68,80,85,102,120,136,170,204,240,255,272,340,408,510,680,816,1020,1360,2040,4080
Greatest Common Factor
We found the factors 748,4080 . The biggest common factor number is the GCF number.
So the greatest common factor 748,4080 is 68.
Lets's calculate LCM of 305,7046
Given numbers has no common factors except 1. So, there LCM is their product i.e 2149030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 68/2149030
Therefore, the GCF of Fractions 748/305,4080/7046 is 68/2149030
Least Common Multiple of 305,7046 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 305,7046 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,7046) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,7046) x common factors =1 x 1 = 1
LCM(305,7046) = ( 305 × 7046 ) / 1
LCM(305,7046) = 2149030 / 1
LCM(305,7046) = 2149030
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FAQs on GCF of Fractions of 748/305, 4080/7046
1. What is the HCF of 748,4080?
The HCF of 748,4080 is 68
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 748/305, 4080/7046?
Answer: GCF of Numerators as per given numbers 748/305, 4080/7046 is
GCF of Numerators i.e. for 748,4080 is 68
LCM of denominators i.e. for 305,7046 is 2149030.
Thus, GCF of Fractions is 68/2149030.Finally, GCF of Fractions for 748/305, 4080/7046 is 68/2149030.