GCF of 218/54, 772/648
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 218/54, 772/648 i.e 2/648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 218/54, 772/648.
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 218/54,772/648?
Given fractions are 218/54,772/648
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 218/54,772/648, numerators are 218,772
Denominators are 54,648
The GCF of 218,772 is 2 .
LCM of 54,648 is 648.
The greatest common factor of 218/54,772/648 = [GCF of 218,772]/[LCM of 54,648]= 2/648
Therefore, the GCF of 218/54,772/648 is 2/648.
To find the highest common factor of 218,772, we have to find the factors of both numbers and list the highest common factor.
The factors of 218 are 1, 2, 109, 218
The factors of 772 are 1, 2, 4, 193, 386, 772
The HCF of 218,772 is 2.
Lets's calculate GCF of 218,772
| 2 | 218, 772 |
| 109, 386 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 218,772 By Matching Biggest Common Factor Method
Now, list down the factors of 218
:1,2,109,218
Now, list down the factors of 772
:1,2,4,193,386,772
Greatest Common Factor
We found the factors 218,772 . The biggest common factor number is the GCF number.
So the greatest common factor 218,772 is 2.
Lets's calculate LCM of 54,648
| 2 | 54, 648 |
| 3 | 27, 324 |
| 3 | 9, 108 |
| 3 | 3, 36 |
| 1, 12 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 1 x 12 = 648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/648
Therefore, the GCF of Fractions 218/54,772/648 is 2/648
Least Common Multiple of 54,648 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 54,648 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,648) = 54
common factors(in case of two or more numbers have common factors) = 1
GCF(54,648) x common factors =54 x 1 = 54
LCM(54,648) = ( 54 × 648 ) / 54
LCM(54,648) = 34992 / 54
LCM(54,648) = 648
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FAQs on GCF of Fractions of 218/54, 772/648
1. What is the HCF of 218,772?
The HCF of 218,772 is 2
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 218/54, 772/648?
Answer: GCF of Numerators as per given numbers 218/54, 772/648 is
GCF of Numerators i.e. for 218,772 is 2
LCM of denominators i.e. for 54,648 is 648.
Thus, GCF of Fractions is 2/648.Finally, GCF of Fractions for 218/54, 772/648 is 2/648.