GCF of 63/168, 30/945, 305/360
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 63/168, 30/945, 305/360 i.e 1/7560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 63/168, 30/945, 305/360.
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 63/168,30/945,305/360?
Given fractions are 63/168,30/945,305/360
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 63/168,30/945,305/360, numerators are 63,30,305
Denominators are 168,945,360
The GCF of 63,30,305 is 1 .
LCM of 168,945,360 is 7560.
The greatest common factor of 63/168,30/945,305/360 = [GCF of 63,30,305]/[LCM of 168,945,360]= 1/7560
Therefore, the GCF of 63/168,30/945,305/360 is 1/7560.
To find the highest common factor of 63,30,305, 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 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 305 are 1, 5, 61, 305
The HCF of 63,30,305 is 1.
Lets's calculate GCF of 63,30,305
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 63,30,305 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 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 305
:1,5,61,305
Greatest Common Factor
We found the factors 63,30,305 . The biggest common factor number is the GCF number.
So the greatest common factor 63,30,305 is 1.
Lets's calculate LCM of 168,945,360
| 2 | 168, 945, 360 |
| 2 | 84, 945, 180 |
| 2 | 42, 945, 90 |
| 3 | 21, 945, 45 |
| 3 | 7, 315, 15 |
| 5 | 7, 105, 5 |
| 7 | 7, 21, 1 |
| 1, 3, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 5 x 7 x 1 x 3 x 1 = 7560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7560
Therefore, the GCF of Fractions 63/168,30/945,305/360 is 1/7560
Least Common Multiple of 168,945,360 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 168,945,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(168,945,360) = 3
common factors(in case of two or more numbers have common factors) = 2520
GCF(168,945,360) x common factors =3 x 2520 = 7560
LCM(168,945,360) = ( 168 × 945 × 360 ) / 7560
LCM(168,945,360) = 57153600 / 7560
LCM(168,945,360) = 7560
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FAQs on GCF of Fractions of 63/168, 30/945, 305/360
1. What is the HCF of 63,30,305?
The HCF of 63,30,305 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 63/168, 30/945, 305/360?
Answer: GCF of Numerators as per given numbers 63/168, 30/945, 305/360 is
GCF of Numerators i.e. for 63,30,305 is 1
LCM of denominators i.e. for 168,945,360 is 7560.
Thus, GCF of Fractions is 1/7560.Finally, GCF of Fractions for 63/168, 30/945, 305/360 is 1/7560.