GCF of 3438/217, 1674/6729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3438/217, 1674/6729 i.e 18/1460193 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3438/217, 1674/6729.
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 3438/217,1674/6729?
Given fractions are 3438/217,1674/6729
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 3438/217,1674/6729, numerators are 3438,1674
Denominators are 217,6729
The GCF of 3438,1674 is 18 .
LCM of 217,6729 is 1460193.
The greatest common factor of 3438/217,1674/6729 = [GCF of 3438,1674]/[LCM of 217,6729]= 18/1460193
Therefore, the GCF of 3438/217,1674/6729 is 18/1460193.
To find the highest common factor of 3438,1674, we have to find the factors of both numbers and list the highest common factor.
The factors of 3438 are 1, 2, 3, 6, 9, 18, 191, 382, 573, 1146, 1719, 3438
The factors of 1674 are 1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837, 1674
The HCF of 3438,1674 is 18.
Lets's calculate GCF of 3438,1674
| 2 | 3438, 1674 |
| 3 | 1719, 837 |
| 3 | 573, 279 |
| 191, 93 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 3438,1674 By Matching Biggest Common Factor Method
Now, list down the factors of 3438
:1,2,3,6,9,18,191,382,573,1146,1719,3438
Now, list down the factors of 1674
:1,2,3,6,9,18,27,31,54,62,93,186,279,558,837,1674
Greatest Common Factor
We found the factors 3438,1674 . The biggest common factor number is the GCF number.
So the greatest common factor 3438,1674 is 18.
Lets's calculate LCM of 217,6729
Given numbers has no common factors except 1. So, there LCM is their product i.e 1460193
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1460193
Therefore, the GCF of Fractions 3438/217,1674/6729 is 18/1460193
Least Common Multiple of 217,6729 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 217,6729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,6729) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,6729) x common factors =1 x 1 = 1
LCM(217,6729) = ( 217 × 6729 ) / 1
LCM(217,6729) = 1460193 / 1
LCM(217,6729) = 1460193
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FAQs on GCF of Fractions of 3438/217, 1674/6729
1. What is the HCF of 3438,1674?
The HCF of 3438,1674 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 3438/217, 1674/6729?
Answer: GCF of Numerators as per given numbers 3438/217, 1674/6729 is
GCF of Numerators i.e. for 3438,1674 is 18
LCM of denominators i.e. for 217,6729 is 1460193.
Thus, GCF of Fractions is 18/1460193.Finally, GCF of Fractions for 3438/217, 1674/6729 is 18/1460193.