GCF of 126/46, 105/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 126/46, 105/674 i.e 21/15502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/46, 105/674.
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 126/46,105/674?
Given fractions are 126/46,105/674
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 126/46,105/674, numerators are 126,105
Denominators are 46,674
The GCF of 126,105 is 21 .
LCM of 46,674 is 15502.
The greatest common factor of 126/46,105/674 = [GCF of 126,105]/[LCM of 46,674]= 21/15502
Therefore, the GCF of 126/46,105/674 is 21/15502.
To find the highest common factor of 126,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 126,105 is 21.
Lets's calculate GCF of 126,105
| 3 | 126, 105 |
| 7 | 42, 35 |
| 6, 5 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 126,105 By Matching Biggest Common Factor Method
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 126,105 . The biggest common factor number is the GCF number.
So the greatest common factor 126,105 is 21.
Lets's calculate LCM of 46,674
| 2 | 46, 674 |
| 23, 337 |
∴ So the LCM of the given numbers is 2 x 23 x 337 = 15502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/15502
Therefore, the GCF of Fractions 126/46,105/674 is 21/15502
Least Common Multiple of 46,674 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 46,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(46,674) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(46,674) x common factors =2 x 1 = 2
LCM(46,674) = ( 46 × 674 ) / 2
LCM(46,674) = 31004 / 2
LCM(46,674) = 15502
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FAQs on GCF of Fractions of 126/46, 105/674
1. What is the HCF of 126,105?
The HCF of 126,105 is 21
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 126/46, 105/674?
Answer: GCF of Numerators as per given numbers 126/46, 105/674 is
GCF of Numerators i.e. for 126,105 is 21
LCM of denominators i.e. for 46,674 is 15502.
Thus, GCF of Fractions is 21/15502.Finally, GCF of Fractions for 126/46, 105/674 is 21/15502.