GCF of 1724/214, 1638/9237
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1724/214, 1638/9237 i.e 2/1976718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1724/214, 1638/9237.
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 1724/214,1638/9237?
Given fractions are 1724/214,1638/9237
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 1724/214,1638/9237, numerators are 1724,1638
Denominators are 214,9237
The GCF of 1724,1638 is 2 .
LCM of 214,9237 is 1976718.
The greatest common factor of 1724/214,1638/9237 = [GCF of 1724,1638]/[LCM of 214,9237]= 2/1976718
Therefore, the GCF of 1724/214,1638/9237 is 2/1976718.
To find the highest common factor of 1724,1638, we have to find the factors of both numbers and list the highest common factor.
The factors of 1724 are 1, 2, 4, 431, 862, 1724
The factors of 1638 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 182, 234, 273, 546, 819, 1638
The HCF of 1724,1638 is 2.
Lets's calculate GCF of 1724,1638
| 2 | 1724, 1638 |
| 862, 819 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1724,1638 By Matching Biggest Common Factor Method
Now, list down the factors of 1724
:1,2,4,431,862,1724
Now, list down the factors of 1638
:1,2,3,6,7,9,13,14,18,21,26,39,42,63,78,91,117,126,182,234,273,546,819,1638
Greatest Common Factor
We found the factors 1724,1638 . The biggest common factor number is the GCF number.
So the greatest common factor 1724,1638 is 2.
Lets's calculate LCM of 214,9237
Given numbers has no common factors except 1. So, there LCM is their product i.e 1976718
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1976718
Therefore, the GCF of Fractions 1724/214,1638/9237 is 2/1976718
Least Common Multiple of 214,9237 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 214,9237 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,9237) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,9237) x common factors =1 x 1 = 1
LCM(214,9237) = ( 214 × 9237 ) / 1
LCM(214,9237) = 1976718 / 1
LCM(214,9237) = 1976718
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FAQs on GCF of Fractions of 1724/214, 1638/9237
1. What is the HCF of 1724,1638?
The HCF of 1724,1638 is 2
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 1724/214, 1638/9237?
Answer: GCF of Numerators as per given numbers 1724/214, 1638/9237 is
GCF of Numerators i.e. for 1724,1638 is 2
LCM of denominators i.e. for 214,9237 is 1976718.
Thus, GCF of Fractions is 2/1976718.Finally, GCF of Fractions for 1724/214, 1638/9237 is 2/1976718.