GCF of 3472/578, 2007/1912
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3472/578, 2007/1912 i.e 1/552568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3472/578, 2007/1912.
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 3472/578,2007/1912?
Given fractions are 3472/578,2007/1912
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 3472/578,2007/1912, numerators are 3472,2007
Denominators are 578,1912
The GCF of 3472,2007 is 1 .
LCM of 578,1912 is 552568.
The greatest common factor of 3472/578,2007/1912 = [GCF of 3472,2007]/[LCM of 578,1912]= 1/552568
Therefore, the GCF of 3472/578,2007/1912 is 1/552568.
To find the highest common factor of 3472,2007, we have to find the factors of both numbers and list the highest common factor.
The factors of 3472 are 1, 2, 4, 7, 8, 14, 16, 28, 31, 56, 62, 112, 124, 217, 248, 434, 496, 868, 1736, 3472
The factors of 2007 are 1, 3, 9, 223, 669, 2007
The HCF of 3472,2007 is 1.
Lets's calculate GCF of 3472,2007
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3472,2007 By Matching Biggest Common Factor Method
Now, list down the factors of 3472
:1,2,4,7,8,14,16,28,31,56,62,112,124,217,248,434,496,868,1736,3472
Now, list down the factors of 2007
:1,3,9,223,669,2007
Greatest Common Factor
We found the factors 3472,2007 . The biggest common factor number is the GCF number.
So the greatest common factor 3472,2007 is 1.
Lets's calculate LCM of 578,1912
| 2 | 578, 1912 |
| 289, 956 |
∴ So the LCM of the given numbers is 2 x 289 x 956 = 552568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/552568
Therefore, the GCF of Fractions 3472/578,2007/1912 is 1/552568
Least Common Multiple of 578,1912 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 578,1912 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,1912) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,1912) x common factors =2 x 1 = 2
LCM(578,1912) = ( 578 × 1912 ) / 2
LCM(578,1912) = 1105136 / 2
LCM(578,1912) = 552568
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FAQs on GCF of Fractions of 3472/578, 2007/1912
1. What is the HCF of 3472,2007?
The HCF of 3472,2007 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 3472/578, 2007/1912?
Answer: GCF of Numerators as per given numbers 3472/578, 2007/1912 is
GCF of Numerators i.e. for 3472,2007 is 1
LCM of denominators i.e. for 578,1912 is 552568.
Thus, GCF of Fractions is 1/552568.Finally, GCF of Fractions for 3472/578, 2007/1912 is 1/552568.