GCF of 63/75, 21/460, 111/642
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 63/75, 21/460, 111/642 i.e 3/738300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 63/75, 21/460, 111/642.
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 63/75,21/460,111/642?
Given fractions are 63/75,21/460,111/642
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 63/75,21/460,111/642, numerators are 63,21,111
Denominators are 75,460,642
The GCF of 63,21,111 is 3 .
LCM of 75,460,642 is 738300.
The greatest common factor of 63/75,21/460,111/642 = [GCF of 63,21,111]/[LCM of 75,460,642]= 3/738300
Therefore, the GCF of 63/75,21/460,111/642 is 3/738300.
To find the highest common factor of 63,21,111, we have to find the factors of both numbers and list the highest common factor.
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 21 are 1, 3, 7, 21
The factors of 111 are 1, 3, 37, 111
The HCF of 63,21,111 is 3.
Lets's calculate GCF of 63,21,111
| 3 | 63, 21, 111 |
| 21, 7, 37 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 63,21,111 By Matching Biggest Common Factor Method
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 111
:1,3,37,111
Greatest Common Factor
We found the factors 63,21,111 . The biggest common factor number is the GCF number.
So the greatest common factor 63,21,111 is 3.
Lets's calculate LCM of 75,460,642
| 2 | 75, 460, 642 |
| 3 | 75, 230, 321 |
| 5 | 25, 230, 107 |
| 5, 46, 107 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 5 x 46 x 107 = 738300
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/738300
Therefore, the GCF of Fractions 63/75,21/460,111/642 is 3/738300
Least Common Multiple of 75,460,642 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 75,460,642 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,460,642) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(75,460,642) x common factors =1 x 30 = 30
LCM(75,460,642) = ( 75 × 460 × 642 ) / 30
LCM(75,460,642) = 22149000 / 30
LCM(75,460,642) = 738300
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FAQs on GCF of Fractions of 63/75, 21/460, 111/642
1. What is the HCF of 63,21,111?
The HCF of 63,21,111 is 3
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 63/75, 21/460, 111/642?
Answer: GCF of Numerators as per given numbers 63/75, 21/460, 111/642 is
GCF of Numerators i.e. for 63,21,111 is 3
LCM of denominators i.e. for 75,460,642 is 738300.
Thus, GCF of Fractions is 3/738300.Finally, GCF of Fractions for 63/75, 21/460, 111/642 is 3/738300.