GCF of 1419/678, 1006/3200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1419/678, 1006/3200 i.e 1/1084800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1419/678, 1006/3200.
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 1419/678,1006/3200?
Given fractions are 1419/678,1006/3200
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 1419/678,1006/3200, numerators are 1419,1006
Denominators are 678,3200
The GCF of 1419,1006 is 1 .
LCM of 678,3200 is 1084800.
The greatest common factor of 1419/678,1006/3200 = [GCF of 1419,1006]/[LCM of 678,3200]= 1/1084800
Therefore, the GCF of 1419/678,1006/3200 is 1/1084800.
To find the highest common factor of 1419,1006, we have to find the factors of both numbers and list the highest common factor.
The factors of 1419 are 1, 3, 11, 33, 43, 129, 473, 1419
The factors of 1006 are 1, 2, 503, 1006
The HCF of 1419,1006 is 1.
Lets's calculate GCF of 1419,1006
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1419,1006 By Matching Biggest Common Factor Method
Now, list down the factors of 1419
:1,3,11,33,43,129,473,1419
Now, list down the factors of 1006
:1,2,503,1006
Greatest Common Factor
We found the factors 1419,1006 . The biggest common factor number is the GCF number.
So the greatest common factor 1419,1006 is 1.
Lets's calculate LCM of 678,3200
| 2 | 678, 3200 |
| 339, 1600 |
∴ So the LCM of the given numbers is 2 x 339 x 1600 = 1084800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1084800
Therefore, the GCF of Fractions 1419/678,1006/3200 is 1/1084800
Least Common Multiple of 678,3200 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 678,3200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,3200) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,3200) x common factors =2 x 1 = 2
LCM(678,3200) = ( 678 × 3200 ) / 2
LCM(678,3200) = 2169600 / 2
LCM(678,3200) = 1084800
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FAQs on GCF of Fractions of 1419/678, 1006/3200
1. What is the HCF of 1419,1006?
The HCF of 1419,1006 is 1
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 1419/678, 1006/3200?
Answer: GCF of Numerators as per given numbers 1419/678, 1006/3200 is
GCF of Numerators i.e. for 1419,1006 is 1
LCM of denominators i.e. for 678,3200 is 1084800.
Thus, GCF of Fractions is 1/1084800.Finally, GCF of Fractions for 1419/678, 1006/3200 is 1/1084800.