GCF of 472/730, 1414/998
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 472/730, 1414/998 i.e 2/364270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 472/730, 1414/998.
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 472/730,1414/998?
Given fractions are 472/730,1414/998
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 472/730,1414/998, numerators are 472,1414
Denominators are 730,998
The GCF of 472,1414 is 2 .
LCM of 730,998 is 364270.
The greatest common factor of 472/730,1414/998 = [GCF of 472,1414]/[LCM of 730,998]= 2/364270
Therefore, the GCF of 472/730,1414/998 is 2/364270.
To find the highest common factor of 472,1414, we have to find the factors of both numbers and list the highest common factor.
The factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472
The factors of 1414 are 1, 2, 7, 14, 101, 202, 707, 1414
The HCF of 472,1414 is 2.
Lets's calculate GCF of 472,1414
| 2 | 472, 1414 |
| 236, 707 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 472,1414 By Matching Biggest Common Factor Method
Now, list down the factors of 472
:1,2,4,8,59,118,236,472
Now, list down the factors of 1414
:1,2,7,14,101,202,707,1414
Greatest Common Factor
We found the factors 472,1414 . The biggest common factor number is the GCF number.
So the greatest common factor 472,1414 is 2.
Lets's calculate LCM of 730,998
| 2 | 730, 998 |
| 365, 499 |
∴ So the LCM of the given numbers is 2 x 365 x 499 = 364270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/364270
Therefore, the GCF of Fractions 472/730,1414/998 is 2/364270
Least Common Multiple of 730,998 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 730,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(730,998) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(730,998) x common factors =2 x 1 = 2
LCM(730,998) = ( 730 × 998 ) / 2
LCM(730,998) = 728540 / 2
LCM(730,998) = 364270
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FAQs on GCF of Fractions of 472/730, 1414/998
1. What is the HCF of 472,1414?
The HCF of 472,1414 is 2
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 472/730, 1414/998?
Answer: GCF of Numerators as per given numbers 472/730, 1414/998 is
GCF of Numerators i.e. for 472,1414 is 2
LCM of denominators i.e. for 730,998 is 364270.
Thus, GCF of Fractions is 2/364270.Finally, GCF of Fractions for 472/730, 1414/998 is 2/364270.