GCF of 648/60, 684/55, 608/56
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 648/60, 684/55, 608/56 i.e 4/9240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 648/60, 684/55, 608/56.
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 648/60,684/55,608/56?
Given fractions are 648/60,684/55,608/56
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 648/60,684/55,608/56, numerators are 648,684,608
Denominators are 60,55,56
The GCF of 648,684,608 is 4 .
LCM of 60,55,56 is 9240.
The greatest common factor of 648/60,684/55,608/56 = [GCF of 648,684,608]/[LCM of 60,55,56]= 4/9240
Therefore, the GCF of 648/60,684/55,608/56 is 4/9240.
To find the highest common factor of 648,684,608, 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 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
The HCF of 648,684,608 is 4.
Lets's calculate GCF of 648,684,608
| 2 | 648, 684, 608 |
| 2 | 324, 342, 304 |
| 162, 171, 152 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 648,684,608 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 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 608
:1,2,4,8,16,19,32,38,76,152,304,608
Greatest Common Factor
We found the factors 648,684,608 . The biggest common factor number is the GCF number.
So the greatest common factor 648,684,608 is 4.
Lets's calculate LCM of 60,55,56
| 2 | 60, 55, 56 |
| 2 | 30, 55, 28 |
| 5 | 15, 55, 14 |
| 3, 11, 14 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 3 x 11 x 14 = 9240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/9240
Therefore, the GCF of Fractions 648/60,684/55,608/56 is 4/9240
Least Common Multiple of 60,55,56 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 60,55,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,55,56) = 1
common factors(in case of two or more numbers have common factors) = 20
GCF(60,55,56) x common factors =1 x 20 = 20
LCM(60,55,56) = ( 60 × 55 × 56 ) / 20
LCM(60,55,56) = 184800 / 20
LCM(60,55,56) = 9240
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 648/60, 684/55, 608/56
1. What is the HCF of 648,684,608?
The HCF of 648,684,608 is 4
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 648/60, 684/55, 608/56?
Answer: GCF of Numerators as per given numbers 648/60, 684/55, 608/56 is
GCF of Numerators i.e. for 648,684,608 is 4
LCM of denominators i.e. for 60,55,56 is 9240.
Thus, GCF of Fractions is 4/9240.Finally, GCF of Fractions for 648/60, 684/55, 608/56 is 4/9240.