GCF of 126/780, 414/390
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 126/780, 414/390 i.e 18/780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/780, 414/390.
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 126/780,414/390?
Given fractions are 126/780,414/390
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 126/780,414/390, numerators are 126,414
Denominators are 780,390
The GCF of 126,414 is 18 .
LCM of 780,390 is 780.
The greatest common factor of 126/780,414/390 = [GCF of 126,414]/[LCM of 780,390]= 18/780
Therefore, the GCF of 126/780,414/390 is 18/780.
To find the highest common factor of 126,414, 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 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 126,414 is 18.
Lets's calculate GCF of 126,414
| 2 | 126, 414 |
| 3 | 63, 207 |
| 3 | 21, 69 |
| 7, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 126,414 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 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 126,414 . The biggest common factor number is the GCF number.
So the greatest common factor 126,414 is 18.
Lets's calculate LCM of 780,390
| 2 | 780, 390 |
| 3 | 390, 195 |
| 5 | 130, 65 |
| 13 | 26, 13 |
| 2, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 2 x 1 = 780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/780
Therefore, the GCF of Fractions 126/780,414/390 is 18/780
Least Common Multiple of 780,390 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 780,390 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,390) = 390
common factors(in case of two or more numbers have common factors) = 1
GCF(780,390) x common factors =390 x 1 = 390
LCM(780,390) = ( 780 × 390 ) / 390
LCM(780,390) = 304200 / 390
LCM(780,390) = 780
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FAQs on GCF of Fractions of 126/780, 414/390
1. What is the HCF of 126,414?
The HCF of 126,414 is 18
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 126/780, 414/390?
Answer: GCF of Numerators as per given numbers 126/780, 414/390 is
GCF of Numerators i.e. for 126,414 is 18
LCM of denominators i.e. for 780,390 is 780.
Thus, GCF of Fractions is 18/780.Finally, GCF of Fractions for 126/780, 414/390 is 18/780.