GCF of 60/419, 7920/4001
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 60/419, 7920/4001 i.e 60/1676419 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/419, 7920/4001.
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 60/419,7920/4001?
Given fractions are 60/419,7920/4001
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 60/419,7920/4001, numerators are 60,7920
Denominators are 419,4001
The GCF of 60,7920 is 60 .
LCM of 419,4001 is 1676419.
The greatest common factor of 60/419,7920/4001 = [GCF of 60,7920]/[LCM of 419,4001]= 60/1676419
Therefore, the GCF of 60/419,7920/4001 is 60/1676419.
To find the highest common factor of 60,7920, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 7920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920
The HCF of 60,7920 is 60.
Lets's calculate GCF of 60,7920
| 2 | 60, 7920 |
| 2 | 30, 3960 |
| 3 | 15, 1980 |
| 5 | 5, 660 |
| 1, 132 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 60,7920 By Matching Biggest Common Factor Method
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 7920
:1,2,3,4,5,6,8,9,10,11,12,15,16,18,20,22,24,30,33,36,40,44,45,48,55,60,66,72,80,88,90,99,110,120,132,144,165,176,180,198,220,240,264,330,360,396,440,495,528,660,720,792,880,990,1320,1584,1980,2640,3960,7920
Greatest Common Factor
We found the factors 60,7920 . The biggest common factor number is the GCF number.
So the greatest common factor 60,7920 is 60.
Lets's calculate LCM of 419,4001
Given numbers has no common factors except 1. So, there LCM is their product i.e 1676419
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/1676419
Therefore, the GCF of Fractions 60/419,7920/4001 is 60/1676419
Least Common Multiple of 419,4001 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 419,4001 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,4001) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,4001) x common factors =1 x 1 = 1
LCM(419,4001) = ( 419 × 4001 ) / 1
LCM(419,4001) = 1676419 / 1
LCM(419,4001) = 1676419
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FAQs on GCF of Fractions of 60/419, 7920/4001
1. What is the HCF of 60,7920?
The HCF of 60,7920 is 60
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 60/419, 7920/4001?
Answer: GCF of Numerators as per given numbers 60/419, 7920/4001 is
GCF of Numerators i.e. for 60,7920 is 60
LCM of denominators i.e. for 419,4001 is 1676419.
Thus, GCF of Fractions is 60/1676419.Finally, GCF of Fractions for 60/419, 7920/4001 is 60/1676419.