GCF of 7029/546, 1689/3918
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7029/546, 1689/3918 i.e 3/356538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7029/546, 1689/3918.
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 7029/546,1689/3918?
Given fractions are 7029/546,1689/3918
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 7029/546,1689/3918, numerators are 7029,1689
Denominators are 546,3918
The GCF of 7029,1689 is 3 .
LCM of 546,3918 is 356538.
The greatest common factor of 7029/546,1689/3918 = [GCF of 7029,1689]/[LCM of 546,3918]= 3/356538
Therefore, the GCF of 7029/546,1689/3918 is 3/356538.
To find the highest common factor of 7029,1689, we have to find the factors of both numbers and list the highest common factor.
The factors of 7029 are 1, 3, 9, 11, 33, 71, 99, 213, 639, 781, 2343, 7029
The factors of 1689 are 1, 3, 563, 1689
The HCF of 7029,1689 is 3.
Lets's calculate GCF of 7029,1689
| 3 | 7029, 1689 |
| 2343, 563 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7029,1689 By Matching Biggest Common Factor Method
Now, list down the factors of 7029
:1,3,9,11,33,71,99,213,639,781,2343,7029
Now, list down the factors of 1689
:1,3,563,1689
Greatest Common Factor
We found the factors 7029,1689 . The biggest common factor number is the GCF number.
So the greatest common factor 7029,1689 is 3.
Lets's calculate LCM of 546,3918
| 2 | 546, 3918 |
| 3 | 273, 1959 |
| 91, 653 |
∴ So the LCM of the given numbers is 2 x 3 x 91 x 653 = 356538
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/356538
Therefore, the GCF of Fractions 7029/546,1689/3918 is 3/356538
Least Common Multiple of 546,3918 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 546,3918 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,3918) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(546,3918) x common factors =6 x 1 = 6
LCM(546,3918) = ( 546 × 3918 ) / 6
LCM(546,3918) = 2139228 / 6
LCM(546,3918) = 356538
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FAQs on GCF of Fractions of 7029/546, 1689/3918
1. What is the HCF of 7029,1689?
The HCF of 7029,1689 is 3
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 7029/546, 1689/3918?
Answer: GCF of Numerators as per given numbers 7029/546, 1689/3918 is
GCF of Numerators i.e. for 7029,1689 is 3
LCM of denominators i.e. for 546,3918 is 356538.
Thus, GCF of Fractions is 3/356538.Finally, GCF of Fractions for 7029/546, 1689/3918 is 3/356538.