GCF of 1632/748, 2671/4214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1632/748, 2671/4214 i.e 1/1576036 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1632/748, 2671/4214.
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 1632/748,2671/4214?
Given fractions are 1632/748,2671/4214
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 1632/748,2671/4214, numerators are 1632,2671
Denominators are 748,4214
The GCF of 1632,2671 is 1 .
LCM of 748,4214 is 1576036.
The greatest common factor of 1632/748,2671/4214 = [GCF of 1632,2671]/[LCM of 748,4214]= 1/1576036
Therefore, the GCF of 1632/748,2671/4214 is 1/1576036.
To find the highest common factor of 1632,2671, we have to find the factors of both numbers and list the highest common factor.
The factors of 1632 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 408, 544, 816, 1632
The factors of 2671 are 1, 2671
The HCF of 1632,2671 is 1.
Lets's calculate GCF of 1632,2671
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1632,2671 By Matching Biggest Common Factor Method
Now, list down the factors of 1632
:1,2,3,4,6,8,12,16,17,24,32,34,48,51,68,96,102,136,204,272,408,544,816,1632
Now, list down the factors of 2671
:1,2671
Greatest Common Factor
We found the factors 1632,2671 . The biggest common factor number is the GCF number.
So the greatest common factor 1632,2671 is 1.
Lets's calculate LCM of 748,4214
| 2 | 748, 4214 |
| 374, 2107 |
∴ So the LCM of the given numbers is 2 x 374 x 2107 = 1576036
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1576036
Therefore, the GCF of Fractions 1632/748,2671/4214 is 1/1576036
Least Common Multiple of 748,4214 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 748,4214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,4214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(748,4214) x common factors =2 x 1 = 2
LCM(748,4214) = ( 748 × 4214 ) / 2
LCM(748,4214) = 3152072 / 2
LCM(748,4214) = 1576036
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FAQs on GCF of Fractions of 1632/748, 2671/4214
1. What is the HCF of 1632,2671?
The HCF of 1632,2671 is 1
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 1632/748, 2671/4214?
Answer: GCF of Numerators as per given numbers 1632/748, 2671/4214 is
GCF of Numerators i.e. for 1632,2671 is 1
LCM of denominators i.e. for 748,4214 is 1576036.
Thus, GCF of Fractions is 1/1576036.Finally, GCF of Fractions for 1632/748, 2671/4214 is 1/1576036.