GCF of 1764/217, 2682/441
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1764/217, 2682/441 i.e 18/13671 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1764/217, 2682/441.
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 1764/217,2682/441?
Given fractions are 1764/217,2682/441
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 1764/217,2682/441, numerators are 1764,2682
Denominators are 217,441
The GCF of 1764,2682 is 18 .
LCM of 217,441 is 13671.
The greatest common factor of 1764/217,2682/441 = [GCF of 1764,2682]/[LCM of 217,441]= 18/13671
Therefore, the GCF of 1764/217,2682/441 is 18/13671.
To find the highest common factor of 1764,2682, we have to find the factors of both numbers and list the highest common factor.
The factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764
The factors of 2682 are 1, 2, 3, 6, 9, 18, 149, 298, 447, 894, 1341, 2682
The HCF of 1764,2682 is 18.
Lets's calculate GCF of 1764,2682
| 2 | 1764, 2682 |
| 3 | 882, 1341 |
| 3 | 294, 447 |
| 98, 149 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 1764,2682 By Matching Biggest Common Factor Method
Now, list down the factors of 1764
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,49,63,84,98,126,147,196,252,294,441,588,882,1764
Now, list down the factors of 2682
:1,2,3,6,9,18,149,298,447,894,1341,2682
Greatest Common Factor
We found the factors 1764,2682 . The biggest common factor number is the GCF number.
So the greatest common factor 1764,2682 is 18.
Lets's calculate LCM of 217,441
| 7 | 217, 441 |
| 31, 63 |
∴ So the LCM of the given numbers is 7 x 31 x 63 = 13671
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/13671
Therefore, the GCF of Fractions 1764/217,2682/441 is 18/13671
Least Common Multiple of 217,441 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 217,441 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,441) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(217,441) x common factors =7 x 1 = 7
LCM(217,441) = ( 217 × 441 ) / 7
LCM(217,441) = 95697 / 7
LCM(217,441) = 13671
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FAQs on GCF of Fractions of 1764/217, 2682/441
1. What is the HCF of 1764,2682?
The HCF of 1764,2682 is 18
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 1764/217, 2682/441?
Answer: GCF of Numerators as per given numbers 1764/217, 2682/441 is
GCF of Numerators i.e. for 1764,2682 is 18
LCM of denominators i.e. for 217,441 is 13671.
Thus, GCF of Fractions is 18/13671.Finally, GCF of Fractions for 1764/217, 2682/441 is 18/13671.