GCF of 6930/233, 1748/164
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6930/233, 1748/164 i.e 2/38212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6930/233, 1748/164.
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 6930/233,1748/164?
Given fractions are 6930/233,1748/164
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 6930/233,1748/164, numerators are 6930,1748
Denominators are 233,164
The GCF of 6930,1748 is 2 .
LCM of 233,164 is 38212.
The greatest common factor of 6930/233,1748/164 = [GCF of 6930,1748]/[LCM of 233,164]= 2/38212
Therefore, the GCF of 6930/233,1748/164 is 2/38212.
To find the highest common factor of 6930,1748, we have to find the factors of both numbers and list the highest common factor.
The factors of 6930 are 1, 2, 3, 5, 6, 7, 9, 10, 11, 14, 15, 18, 21, 22, 30, 33, 35, 42, 45, 55, 63, 66, 70, 77, 90, 99, 105, 110, 126, 154, 165, 198, 210, 231, 315, 330, 385, 462, 495, 630, 693, 770, 990, 1155, 1386, 2310, 3465, 6930
The factors of 1748 are 1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748
The HCF of 6930,1748 is 2.
Lets's calculate GCF of 6930,1748
| 2 | 6930, 1748 |
| 3465, 874 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6930,1748 By Matching Biggest Common Factor Method
Now, list down the factors of 6930
:1,2,3,5,6,7,9,10,11,14,15,18,21,22,30,33,35,42,45,55,63,66,70,77,90,99,105,110,126,154,165,198,210,231,315,330,385,462,495,630,693,770,990,1155,1386,2310,3465,6930
Now, list down the factors of 1748
:1,2,4,19,23,38,46,76,92,437,874,1748
Greatest Common Factor
We found the factors 6930,1748 . The biggest common factor number is the GCF number.
So the greatest common factor 6930,1748 is 2.
Lets's calculate LCM of 233,164
Given numbers has no common factors except 1. So, there LCM is their product i.e 38212
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38212
Therefore, the GCF of Fractions 6930/233,1748/164 is 2/38212
Least Common Multiple of 233,164 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 233,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(233,164) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(233,164) x common factors =1 x 1 = 1
LCM(233,164) = ( 233 × 164 ) / 1
LCM(233,164) = 38212 / 1
LCM(233,164) = 38212
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FAQs on GCF of Fractions of 6930/233, 1748/164
1. What is the HCF of 6930,1748?
The HCF of 6930,1748 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 6930/233, 1748/164?
Answer: GCF of Numerators as per given numbers 6930/233, 1748/164 is
GCF of Numerators i.e. for 6930,1748 is 2
LCM of denominators i.e. for 233,164 is 38212.
Thus, GCF of Fractions is 2/38212.Finally, GCF of Fractions for 6930/233, 1748/164 is 2/38212.