GCF of 189/22, 306/70, 105/49
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 189/22, 306/70, 105/49 i.e 3/5390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/22, 306/70, 105/49.
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 189/22,306/70,105/49?
Given fractions are 189/22,306/70,105/49
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 189/22,306/70,105/49, numerators are 189,306,105
Denominators are 22,70,49
The GCF of 189,306,105 is 3 .
LCM of 22,70,49 is 5390.
The greatest common factor of 189/22,306/70,105/49 = [GCF of 189,306,105]/[LCM of 22,70,49]= 3/5390
Therefore, the GCF of 189/22,306/70,105/49 is 3/5390.
To find the highest common factor of 189,306,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 189,306,105 is 3.
Lets's calculate GCF of 189,306,105
| 3 | 189, 306, 105 |
| 63, 102, 35 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 189,306,105 By Matching Biggest Common Factor Method
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 189,306,105 . The biggest common factor number is the GCF number.
So the greatest common factor 189,306,105 is 3.
Lets's calculate LCM of 22,70,49
| 2 | 22, 70, 49 |
| 7 | 11, 35, 49 |
| 11, 5, 7 |
∴ So the LCM of the given numbers is 2 x 7 x 11 x 5 x 7 = 5390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5390
Therefore, the GCF of Fractions 189/22,306/70,105/49 is 3/5390
Least Common Multiple of 22,70,49 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 22,70,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(22,70,49) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(22,70,49) x common factors =1 x 14 = 14
LCM(22,70,49) = ( 22 × 70 × 49 ) / 14
LCM(22,70,49) = 75460 / 14
LCM(22,70,49) = 5390
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FAQs on GCF of Fractions of 189/22, 306/70, 105/49
1. What is the HCF of 189,306,105?
The HCF of 189,306,105 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 189/22, 306/70, 105/49?
Answer: GCF of Numerators as per given numbers 189/22, 306/70, 105/49 is
GCF of Numerators i.e. for 189,306,105 is 3
LCM of denominators i.e. for 22,70,49 is 5390.
Thus, GCF of Fractions is 3/5390.Finally, GCF of Fractions for 189/22, 306/70, 105/49 is 3/5390.