GCF of 3627/228, 1683/516
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3627/228, 1683/516 i.e 9/9804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3627/228, 1683/516.
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 3627/228,1683/516?
Given fractions are 3627/228,1683/516
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 3627/228,1683/516, numerators are 3627,1683
Denominators are 228,516
The GCF of 3627,1683 is 9 .
LCM of 228,516 is 9804.
The greatest common factor of 3627/228,1683/516 = [GCF of 3627,1683]/[LCM of 228,516]= 9/9804
Therefore, the GCF of 3627/228,1683/516 is 9/9804.
To find the highest common factor of 3627,1683, we have to find the factors of both numbers and list the highest common factor.
The factors of 3627 are 1, 3, 9, 13, 31, 39, 93, 117, 279, 403, 1209, 3627
The factors of 1683 are 1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683
The HCF of 3627,1683 is 9.
Lets's calculate GCF of 3627,1683
| 3 | 3627, 1683 |
| 3 | 1209, 561 |
| 403, 187 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 3627,1683 By Matching Biggest Common Factor Method
Now, list down the factors of 3627
:1,3,9,13,31,39,93,117,279,403,1209,3627
Now, list down the factors of 1683
:1,3,9,11,17,33,51,99,153,187,561,1683
Greatest Common Factor
We found the factors 3627,1683 . The biggest common factor number is the GCF number.
So the greatest common factor 3627,1683 is 9.
Lets's calculate LCM of 228,516
| 2 | 228, 516 |
| 2 | 114, 258 |
| 3 | 57, 129 |
| 19, 43 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 43 = 9804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/9804
Therefore, the GCF of Fractions 3627/228,1683/516 is 9/9804
Least Common Multiple of 228,516 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 228,516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(228,516) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(228,516) x common factors =12 x 1 = 12
LCM(228,516) = ( 228 × 516 ) / 12
LCM(228,516) = 117648 / 12
LCM(228,516) = 9804
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FAQs on GCF of Fractions of 3627/228, 1683/516
1. What is the HCF of 3627,1683?
The HCF of 3627,1683 is 9
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 3627/228, 1683/516?
Answer: GCF of Numerators as per given numbers 3627/228, 1683/516 is
GCF of Numerators i.e. for 3627,1683 is 9
LCM of denominators i.e. for 228,516 is 9804.
Thus, GCF of Fractions is 9/9804.Finally, GCF of Fractions for 3627/228, 1683/516 is 9/9804.