GCF of 1218/217, 7665/1722
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1218/217, 7665/1722 i.e 21/53382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1218/217, 7665/1722.
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 1218/217,7665/1722?
Given fractions are 1218/217,7665/1722
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 1218/217,7665/1722, numerators are 1218,7665
Denominators are 217,1722
The GCF of 1218,7665 is 21 .
LCM of 217,1722 is 53382.
The greatest common factor of 1218/217,7665/1722 = [GCF of 1218,7665]/[LCM of 217,1722]= 21/53382
Therefore, the GCF of 1218/217,7665/1722 is 21/53382.
To find the highest common factor of 1218,7665, we have to find the factors of both numbers and list the highest common factor.
The factors of 1218 are 1, 2, 3, 6, 7, 14, 21, 29, 42, 58, 87, 174, 203, 406, 609, 1218
The factors of 7665 are 1, 3, 5, 7, 15, 21, 35, 73, 105, 219, 365, 511, 1095, 1533, 2555, 7665
The HCF of 1218,7665 is 21.
Lets's calculate GCF of 1218,7665
| 3 | 1218, 7665 |
| 7 | 406, 2555 |
| 58, 365 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 1218,7665 By Matching Biggest Common Factor Method
Now, list down the factors of 1218
:1,2,3,6,7,14,21,29,42,58,87,174,203,406,609,1218
Now, list down the factors of 7665
:1,3,5,7,15,21,35,73,105,219,365,511,1095,1533,2555,7665
Greatest Common Factor
We found the factors 1218,7665 . The biggest common factor number is the GCF number.
So the greatest common factor 1218,7665 is 21.
Lets's calculate LCM of 217,1722
| 7 | 217, 1722 |
| 31, 246 |
∴ So the LCM of the given numbers is 7 x 31 x 246 = 53382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/53382
Therefore, the GCF of Fractions 1218/217,7665/1722 is 21/53382
Least Common Multiple of 217,1722 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 217,1722 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,1722) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(217,1722) x common factors =7 x 1 = 7
LCM(217,1722) = ( 217 × 1722 ) / 7
LCM(217,1722) = 373674 / 7
LCM(217,1722) = 53382
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FAQs on GCF of Fractions of 1218/217, 7665/1722
1. What is the HCF of 1218,7665?
The HCF of 1218,7665 is 21
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 1218/217, 7665/1722?
Answer: GCF of Numerators as per given numbers 1218/217, 7665/1722 is
GCF of Numerators i.e. for 1218,7665 is 21
LCM of denominators i.e. for 217,1722 is 53382.
Thus, GCF of Fractions is 21/53382.Finally, GCF of Fractions for 1218/217, 7665/1722 is 21/53382.