GCF of 4218/210, 9975/7071
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4218/210, 9975/7071 i.e 57/494970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4218/210, 9975/7071.
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 4218/210,9975/7071?
Given fractions are 4218/210,9975/7071
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 4218/210,9975/7071, numerators are 4218,9975
Denominators are 210,7071
The GCF of 4218,9975 is 57 .
LCM of 210,7071 is 494970.
The greatest common factor of 4218/210,9975/7071 = [GCF of 4218,9975]/[LCM of 210,7071]= 57/494970
Therefore, the GCF of 4218/210,9975/7071 is 57/494970.
To find the highest common factor of 4218,9975, we have to find the factors of both numbers and list the highest common factor.
The factors of 4218 are 1, 2, 3, 6, 19, 37, 38, 57, 74, 111, 114, 222, 703, 1406, 2109, 4218
The factors of 9975 are 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975
The HCF of 4218,9975 is 57.
Lets's calculate GCF of 4218,9975
| 3 | 4218, 9975 |
| 19 | 1406, 3325 |
| 74, 175 |
∴ So the GCF of the given numbers is 3 x 19 = 57
Greatest Common Factor of 4218,9975 By Matching Biggest Common Factor Method
Now, list down the factors of 4218
:1,2,3,6,19,37,38,57,74,111,114,222,703,1406,2109,4218
Now, list down the factors of 9975
:1,3,5,7,15,19,21,25,35,57,75,95,105,133,175,285,399,475,525,665,1425,1995,3325,9975
Greatest Common Factor
We found the factors 4218,9975 . The biggest common factor number is the GCF number.
So the greatest common factor 4218,9975 is 57.
Lets's calculate LCM of 210,7071
| 3 | 210, 7071 |
| 70, 2357 |
∴ So the LCM of the given numbers is 3 x 70 x 2357 = 494970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/494970
Therefore, the GCF of Fractions 4218/210,9975/7071 is 57/494970
Least Common Multiple of 210,7071 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 210,7071 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(210,7071) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(210,7071) x common factors =3 x 1 = 3
LCM(210,7071) = ( 210 × 7071 ) / 3
LCM(210,7071) = 1484910 / 3
LCM(210,7071) = 494970
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FAQs on GCF of Fractions of 4218/210, 9975/7071
1. What is the HCF of 4218,9975?
The HCF of 4218,9975 is 57
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 4218/210, 9975/7071?
Answer: GCF of Numerators as per given numbers 4218/210, 9975/7071 is
GCF of Numerators i.e. for 4218,9975 is 57
LCM of denominators i.e. for 210,7071 is 494970.
Thus, GCF of Fractions is 57/494970.Finally, GCF of Fractions for 4218/210, 9975/7071 is 57/494970.