GCF of 21/42, 578/75, 612/204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/42, 578/75, 612/204 i.e 1/35700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/42, 578/75, 612/204.
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 21/42,578/75,612/204?
Given fractions are 21/42,578/75,612/204
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 21/42,578/75,612/204, numerators are 21,578,612
Denominators are 42,75,204
The GCF of 21,578,612 is 1 .
LCM of 42,75,204 is 35700.
The greatest common factor of 21/42,578/75,612/204 = [GCF of 21,578,612]/[LCM of 42,75,204]= 1/35700
Therefore, the GCF of 21/42,578/75,612/204 is 1/35700.
To find the highest common factor of 21,578,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 21,578,612 is 1.
Lets's calculate GCF of 21,578,612
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,578,612 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 21,578,612 . The biggest common factor number is the GCF number.
So the greatest common factor 21,578,612 is 1.
Lets's calculate LCM of 42,75,204
| 2 | 42, 75, 204 |
| 3 | 21, 75, 102 |
| 7, 25, 34 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 25 x 34 = 35700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35700
Therefore, the GCF of Fractions 21/42,578/75,612/204 is 1/35700
Least Common Multiple of 42,75,204 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 42,75,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,75,204) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(42,75,204) x common factors =3 x 6 = 18
LCM(42,75,204) = ( 42 × 75 × 204 ) / 18
LCM(42,75,204) = 642600 / 18
LCM(42,75,204) = 35700
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FAQs on GCF of Fractions of 21/42, 578/75, 612/204
1. What is the HCF of 21,578,612?
The HCF of 21,578,612 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 21/42, 578/75, 612/204?
Answer: GCF of Numerators as per given numbers 21/42, 578/75, 612/204 is
GCF of Numerators i.e. for 21,578,612 is 1
LCM of denominators i.e. for 42,75,204 is 35700.
Thus, GCF of Fractions is 1/35700.Finally, GCF of Fractions for 21/42, 578/75, 612/204 is 1/35700.