GCF of 1412/762, 5904/3189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1412/762, 5904/3189 i.e 4/810006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1412/762, 5904/3189.
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 1412/762,5904/3189?
Given fractions are 1412/762,5904/3189
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 1412/762,5904/3189, numerators are 1412,5904
Denominators are 762,3189
The GCF of 1412,5904 is 4 .
LCM of 762,3189 is 810006.
The greatest common factor of 1412/762,5904/3189 = [GCF of 1412,5904]/[LCM of 762,3189]= 4/810006
Therefore, the GCF of 1412/762,5904/3189 is 4/810006.
To find the highest common factor of 1412,5904, we have to find the factors of both numbers and list the highest common factor.
The factors of 1412 are 1, 2, 4, 353, 706, 1412
The factors of 5904 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 41, 48, 72, 82, 123, 144, 164, 246, 328, 369, 492, 656, 738, 984, 1476, 1968, 2952, 5904
The HCF of 1412,5904 is 4.
Lets's calculate GCF of 1412,5904
| 2 | 1412, 5904 |
| 2 | 706, 2952 |
| 353, 1476 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 1412,5904 By Matching Biggest Common Factor Method
Now, list down the factors of 1412
:1,2,4,353,706,1412
Now, list down the factors of 5904
:1,2,3,4,6,8,9,12,16,18,24,36,41,48,72,82,123,144,164,246,328,369,492,656,738,984,1476,1968,2952,5904
Greatest Common Factor
We found the factors 1412,5904 . The biggest common factor number is the GCF number.
So the greatest common factor 1412,5904 is 4.
Lets's calculate LCM of 762,3189
| 3 | 762, 3189 |
| 254, 1063 |
∴ So the LCM of the given numbers is 3 x 254 x 1063 = 810006
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/810006
Therefore, the GCF of Fractions 1412/762,5904/3189 is 4/810006
Least Common Multiple of 762,3189 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 762,3189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(762,3189) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(762,3189) x common factors =3 x 1 = 3
LCM(762,3189) = ( 762 × 3189 ) / 3
LCM(762,3189) = 2430018 / 3
LCM(762,3189) = 810006
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FAQs on GCF of Fractions of 1412/762, 5904/3189
1. What is the HCF of 1412,5904?
The HCF of 1412,5904 is 4
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 1412/762, 5904/3189?
Answer: GCF of Numerators as per given numbers 1412/762, 5904/3189 is
GCF of Numerators i.e. for 1412,5904 is 4
LCM of denominators i.e. for 762,3189 is 810006.
Thus, GCF of Fractions is 4/810006.Finally, GCF of Fractions for 1412/762, 5904/3189 is 4/810006.