GCF of 648/654, 3450/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 648/654, 3450/315 i.e 6/68670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 648/654, 3450/315.
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 648/654,3450/315?
Given fractions are 648/654,3450/315
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 648/654,3450/315, numerators are 648,3450
Denominators are 654,315
The GCF of 648,3450 is 6 .
LCM of 654,315 is 68670.
The greatest common factor of 648/654,3450/315 = [GCF of 648,3450]/[LCM of 654,315]= 6/68670
Therefore, the GCF of 648/654,3450/315 is 6/68670.
To find the highest common factor of 648,3450, we have to find the factors of both numbers and list the highest common factor.
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The factors of 3450 are 1, 2, 3, 5, 6, 10, 15, 23, 25, 30, 46, 50, 69, 75, 115, 138, 150, 230, 345, 575, 690, 1150, 1725, 3450
The HCF of 648,3450 is 6.
Lets's calculate GCF of 648,3450
| 2 | 648, 3450 |
| 3 | 324, 1725 |
| 108, 575 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 648,3450 By Matching Biggest Common Factor Method
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Now, list down the factors of 3450
:1,2,3,5,6,10,15,23,25,30,46,50,69,75,115,138,150,230,345,575,690,1150,1725,3450
Greatest Common Factor
We found the factors 648,3450 . The biggest common factor number is the GCF number.
So the greatest common factor 648,3450 is 6.
Lets's calculate LCM of 654,315
| 3 | 654, 315 |
| 218, 105 |
∴ So the LCM of the given numbers is 3 x 218 x 105 = 68670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/68670
Therefore, the GCF of Fractions 648/654,3450/315 is 6/68670
Least Common Multiple of 654,315 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 654,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(654,315) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(654,315) x common factors =3 x 1 = 3
LCM(654,315) = ( 654 × 315 ) / 3
LCM(654,315) = 206010 / 3
LCM(654,315) = 68670
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FAQs on GCF of Fractions of 648/654, 3450/315
1. What is the HCF of 648,3450?
The HCF of 648,3450 is 6
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 648/654, 3450/315?
Answer: GCF of Numerators as per given numbers 648/654, 3450/315 is
GCF of Numerators i.e. for 648,3450 is 6
LCM of denominators i.e. for 654,315 is 68670.
Thus, GCF of Fractions is 6/68670.Finally, GCF of Fractions for 648/654, 3450/315 is 6/68670.