GCF of 148/60, 960/85, 546/64
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 148/60, 960/85, 546/64 i.e 2/16320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 148/60, 960/85, 546/64.
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 148/60,960/85,546/64?
Given fractions are 148/60,960/85,546/64
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 148/60,960/85,546/64, numerators are 148,960,546
Denominators are 60,85,64
The GCF of 148,960,546 is 2 .
LCM of 60,85,64 is 16320.
The greatest common factor of 148/60,960/85,546/64 = [GCF of 148,960,546]/[LCM of 60,85,64]= 2/16320
Therefore, the GCF of 148/60,960/85,546/64 is 2/16320.
To find the highest common factor of 148,960,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 148 are 1, 2, 4, 37, 74, 148
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 148,960,546 is 2.
Lets's calculate GCF of 148,960,546
| 2 | 148, 960, 546 |
| 74, 480, 273 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 148,960,546 By Matching Biggest Common Factor Method
Now, list down the factors of 148
:1,2,4,37,74,148
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 148,960,546 . The biggest common factor number is the GCF number.
So the greatest common factor 148,960,546 is 2.
Lets's calculate LCM of 60,85,64
| 2 | 60, 85, 64 |
| 2 | 30, 85, 32 |
| 5 | 15, 85, 16 |
| 3, 17, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 3 x 17 x 16 = 16320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16320
Therefore, the GCF of Fractions 148/60,960/85,546/64 is 2/16320
Least Common Multiple of 60,85,64 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 60,85,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,85,64) = 1
common factors(in case of two or more numbers have common factors) = 20
GCF(60,85,64) x common factors =1 x 20 = 20
LCM(60,85,64) = ( 60 × 85 × 64 ) / 20
LCM(60,85,64) = 326400 / 20
LCM(60,85,64) = 16320
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FAQs on GCF of Fractions of 148/60, 960/85, 546/64
1. What is the HCF of 148,960,546?
The HCF of 148,960,546 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 148/60, 960/85, 546/64?
Answer: GCF of Numerators as per given numbers 148/60, 960/85, 546/64 is
GCF of Numerators i.e. for 148,960,546 is 2
LCM of denominators i.e. for 60,85,64 is 16320.
Thus, GCF of Fractions is 2/16320.Finally, GCF of Fractions for 148/60, 960/85, 546/64 is 2/16320.