GCF of 192/126, 1716/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 192/126, 1716/105 i.e 12/630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 192/126, 1716/105.
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 192/126,1716/105?
Given fractions are 192/126,1716/105
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 192/126,1716/105, numerators are 192,1716
Denominators are 126,105
The GCF of 192,1716 is 12 .
LCM of 126,105 is 630.
The greatest common factor of 192/126,1716/105 = [GCF of 192,1716]/[LCM of 126,105]= 12/630
Therefore, the GCF of 192/126,1716/105 is 12/630.
To find the highest common factor of 192,1716, we have to find the factors of both numbers and list the highest common factor.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The factors of 1716 are 1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 44, 52, 66, 78, 132, 143, 156, 286, 429, 572, 858, 1716
The HCF of 192,1716 is 12.
Lets's calculate GCF of 192,1716
| 2 | 192, 1716 |
| 2 | 96, 858 |
| 3 | 48, 429 |
| 16, 143 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 192,1716 By Matching Biggest Common Factor Method
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Now, list down the factors of 1716
:1,2,3,4,6,11,12,13,22,26,33,39,44,52,66,78,132,143,156,286,429,572,858,1716
Greatest Common Factor
We found the factors 192,1716 . The biggest common factor number is the GCF number.
So the greatest common factor 192,1716 is 12.
Lets's calculate LCM of 126,105
| 3 | 126, 105 |
| 7 | 42, 35 |
| 6, 5 |
∴ So the LCM of the given numbers is 3 x 7 x 6 x 5 = 630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/630
Therefore, the GCF of Fractions 192/126,1716/105 is 12/630
Least Common Multiple of 126,105 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 126,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(126,105) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(126,105) x common factors =21 x 1 = 21
LCM(126,105) = ( 126 × 105 ) / 21
LCM(126,105) = 13230 / 21
LCM(126,105) = 630
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FAQs on GCF of Fractions of 192/126, 1716/105
1. What is the HCF of 192,1716?
The HCF of 192,1716 is 12
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 192/126, 1716/105?
Answer: GCF of Numerators as per given numbers 192/126, 1716/105 is
GCF of Numerators i.e. for 192,1716 is 12
LCM of denominators i.e. for 126,105 is 630.
Thus, GCF of Fractions is 12/630.Finally, GCF of Fractions for 192/126, 1716/105 is 12/630.