GCF of 1682/830, 6728/2253
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1682/830, 6728/2253 i.e 1682/1869990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1682/830, 6728/2253.
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 1682/830,6728/2253?
Given fractions are 1682/830,6728/2253
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 1682/830,6728/2253, numerators are 1682,6728
Denominators are 830,2253
The GCF of 1682,6728 is 1682 .
LCM of 830,2253 is 1869990.
The greatest common factor of 1682/830,6728/2253 = [GCF of 1682,6728]/[LCM of 830,2253]= 1682/1869990
Therefore, the GCF of 1682/830,6728/2253 is 1682/1869990.
To find the highest common factor of 1682,6728, we have to find the factors of both numbers and list the highest common factor.
The factors of 1682 are 1, 2, 29, 58, 841, 1682
The factors of 6728 are 1, 2, 4, 8, 29, 58, 116, 232, 841, 1682, 3364, 6728
The HCF of 1682,6728 is 1682.
Lets's calculate GCF of 1682,6728
| 2 | 1682, 6728 |
| 29 | 841, 3364 |
| 29 | 29, 116 |
| 1, 4 |
∴ So the GCF of the given numbers is 2 x 29 x 29 = 1682
Greatest Common Factor of 1682,6728 By Matching Biggest Common Factor Method
Now, list down the factors of 1682
:1,2,29,58,841,1682
Now, list down the factors of 6728
:1,2,4,8,29,58,116,232,841,1682,3364,6728
Greatest Common Factor
We found the factors 1682,6728 . The biggest common factor number is the GCF number.
So the greatest common factor 1682,6728 is 1682.
Lets's calculate LCM of 830,2253
Given numbers has no common factors except 1. So, there LCM is their product i.e 1869990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1682/1869990
Therefore, the GCF of Fractions 1682/830,6728/2253 is 1682/1869990
Least Common Multiple of 830,2253 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 830,2253 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(830,2253) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(830,2253) x common factors =1 x 1 = 1
LCM(830,2253) = ( 830 × 2253 ) / 1
LCM(830,2253) = 1869990 / 1
LCM(830,2253) = 1869990
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FAQs on GCF of Fractions of 1682/830, 6728/2253
1. What is the HCF of 1682,6728?
The HCF of 1682,6728 is 1682
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 1682/830, 6728/2253?
Answer: GCF of Numerators as per given numbers 1682/830, 6728/2253 is
GCF of Numerators i.e. for 1682,6728 is 1682
LCM of denominators i.e. for 830,2253 is 1869990.
Thus, GCF of Fractions is 1682/1869990.Finally, GCF of Fractions for 1682/830, 6728/2253 is 1682/1869990.