GCF of 46/408, 80/153, 654/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/408, 80/153, 654/978 i.e 2/199512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/408, 80/153, 654/978.
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 46/408,80/153,654/978?
Given fractions are 46/408,80/153,654/978
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 46/408,80/153,654/978, numerators are 46,80,654
Denominators are 408,153,978
The GCF of 46,80,654 is 2 .
LCM of 408,153,978 is 199512.
The greatest common factor of 46/408,80/153,654/978 = [GCF of 46,80,654]/[LCM of 408,153,978]= 2/199512
Therefore, the GCF of 46/408,80/153,654/978 is 2/199512.
To find the highest common factor of 46,80,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 46,80,654 is 2.
Lets's calculate GCF of 46,80,654
| 2 | 46, 80, 654 |
| 23, 40, 327 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 46,80,654 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 46,80,654 . The biggest common factor number is the GCF number.
So the greatest common factor 46,80,654 is 2.
Lets's calculate LCM of 408,153,978
| 2 | 408, 153, 978 |
| 3 | 204, 153, 489 |
| 17 | 68, 51, 163 |
| 4, 3, 163 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 4 x 3 x 163 = 199512
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/199512
Therefore, the GCF of Fractions 46/408,80/153,654/978 is 2/199512
Least Common Multiple of 408,153,978 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 408,153,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,153,978) = 3
common factors(in case of two or more numbers have common factors) = 102
GCF(408,153,978) x common factors =3 x 102 = 306
LCM(408,153,978) = ( 408 × 153 × 978 ) / 306
LCM(408,153,978) = 61050672 / 306
LCM(408,153,978) = 199512
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FAQs on GCF of Fractions of 46/408, 80/153, 654/978
1. What is the HCF of 46,80,654?
The HCF of 46,80,654 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 46/408, 80/153, 654/978?
Answer: GCF of Numerators as per given numbers 46/408, 80/153, 654/978 is
GCF of Numerators i.e. for 46,80,654 is 2
LCM of denominators i.e. for 408,153,978 is 199512.
Thus, GCF of Fractions is 2/199512.Finally, GCF of Fractions for 46/408, 80/153, 654/978 is 2/199512.