GCF of 1947/306, 3658/3054
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1947/306, 3658/3054 i.e 59/155754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1947/306, 3658/3054.
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 1947/306,3658/3054?
Given fractions are 1947/306,3658/3054
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 1947/306,3658/3054, numerators are 1947,3658
Denominators are 306,3054
The GCF of 1947,3658 is 59 .
LCM of 306,3054 is 155754.
The greatest common factor of 1947/306,3658/3054 = [GCF of 1947,3658]/[LCM of 306,3054]= 59/155754
Therefore, the GCF of 1947/306,3658/3054 is 59/155754.
To find the highest common factor of 1947,3658, we have to find the factors of both numbers and list the highest common factor.
The factors of 1947 are 1, 3, 11, 33, 59, 177, 649, 1947
The factors of 3658 are 1, 2, 31, 59, 62, 118, 1829, 3658
The HCF of 1947,3658 is 59.
Lets's calculate GCF of 1947,3658
| 59 | 1947, 3658 |
| 33, 62 |
∴ So the GCF of the given numbers is 59 = 59
Greatest Common Factor of 1947,3658 By Matching Biggest Common Factor Method
Now, list down the factors of 1947
:1,3,11,33,59,177,649,1947
Now, list down the factors of 3658
:1,2,31,59,62,118,1829,3658
Greatest Common Factor
We found the factors 1947,3658 . The biggest common factor number is the GCF number.
So the greatest common factor 1947,3658 is 59.
Lets's calculate LCM of 306,3054
| 2 | 306, 3054 |
| 3 | 153, 1527 |
| 51, 509 |
∴ So the LCM of the given numbers is 2 x 3 x 51 x 509 = 155754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 59/155754
Therefore, the GCF of Fractions 1947/306,3658/3054 is 59/155754
Least Common Multiple of 306,3054 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 306,3054 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,3054) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(306,3054) x common factors =6 x 1 = 6
LCM(306,3054) = ( 306 × 3054 ) / 6
LCM(306,3054) = 934524 / 6
LCM(306,3054) = 155754
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1947/306, 3658/3054
1. What is the HCF of 1947,3658?
The HCF of 1947,3658 is 59
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 1947/306, 3658/3054?
Answer: GCF of Numerators as per given numbers 1947/306, 3658/3054 is
GCF of Numerators i.e. for 1947,3658 is 59
LCM of denominators i.e. for 306,3054 is 155754.
Thus, GCF of Fractions is 59/155754.Finally, GCF of Fractions for 1947/306, 3658/3054 is 59/155754.