GCF of 7100/164, 1648/1719
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7100/164, 1648/1719 i.e 4/281916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7100/164, 1648/1719.
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 7100/164,1648/1719?
Given fractions are 7100/164,1648/1719
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 7100/164,1648/1719, numerators are 7100,1648
Denominators are 164,1719
The GCF of 7100,1648 is 4 .
LCM of 164,1719 is 281916.
The greatest common factor of 7100/164,1648/1719 = [GCF of 7100,1648]/[LCM of 164,1719]= 4/281916
Therefore, the GCF of 7100/164,1648/1719 is 4/281916.
To find the highest common factor of 7100,1648, we have to find the factors of both numbers and list the highest common factor.
The factors of 7100 are 1, 2, 4, 5, 10, 20, 25, 50, 71, 100, 142, 284, 355, 710, 1420, 1775, 3550, 7100
The factors of 1648 are 1, 2, 4, 8, 16, 103, 206, 412, 824, 1648
The HCF of 7100,1648 is 4.
Lets's calculate GCF of 7100,1648
| 2 | 7100, 1648 |
| 2 | 3550, 824 |
| 1775, 412 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7100,1648 By Matching Biggest Common Factor Method
Now, list down the factors of 7100
:1,2,4,5,10,20,25,50,71,100,142,284,355,710,1420,1775,3550,7100
Now, list down the factors of 1648
:1,2,4,8,16,103,206,412,824,1648
Greatest Common Factor
We found the factors 7100,1648 . The biggest common factor number is the GCF number.
So the greatest common factor 7100,1648 is 4.
Lets's calculate LCM of 164,1719
Given numbers has no common factors except 1. So, there LCM is their product i.e 281916
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/281916
Therefore, the GCF of Fractions 7100/164,1648/1719 is 4/281916
Least Common Multiple of 164,1719 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 164,1719 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,1719) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(164,1719) x common factors =1 x 1 = 1
LCM(164,1719) = ( 164 × 1719 ) / 1
LCM(164,1719) = 281916 / 1
LCM(164,1719) = 281916
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FAQs on GCF of Fractions of 7100/164, 1648/1719
1. What is the HCF of 7100,1648?
The HCF of 7100,1648 is 4
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 7100/164, 1648/1719?
Answer: GCF of Numerators as per given numbers 7100/164, 1648/1719 is
GCF of Numerators i.e. for 7100,1648 is 4
LCM of denominators i.e. for 164,1719 is 281916.
Thus, GCF of Fractions is 4/281916.Finally, GCF of Fractions for 7100/164, 1648/1719 is 4/281916.