GCF of 5880/205, 4140/1002
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5880/205, 4140/1002 i.e 60/205410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5880/205, 4140/1002.
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 5880/205,4140/1002?
Given fractions are 5880/205,4140/1002
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 5880/205,4140/1002, numerators are 5880,4140
Denominators are 205,1002
The GCF of 5880,4140 is 60 .
LCM of 205,1002 is 205410.
The greatest common factor of 5880/205,4140/1002 = [GCF of 5880,4140]/[LCM of 205,1002]= 60/205410
Therefore, the GCF of 5880/205,4140/1002 is 60/205410.
To find the highest common factor of 5880,4140, we have to find the factors of both numbers and list the highest common factor.
The factors of 5880 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, 392, 420, 490, 588, 735, 840, 980, 1176, 1470, 1960, 2940, 5880
The factors of 4140 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070, 4140
The HCF of 5880,4140 is 60.
Lets's calculate GCF of 5880,4140
| 2 | 5880, 4140 |
| 2 | 2940, 2070 |
| 3 | 1470, 1035 |
| 5 | 490, 345 |
| 98, 69 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 5880,4140 By Matching Biggest Common Factor Method
Now, list down the factors of 5880
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,49,56,60,70,84,98,105,120,140,147,168,196,210,245,280,294,392,420,490,588,735,840,980,1176,1470,1960,2940,5880
Now, list down the factors of 4140
:1,2,3,4,5,6,9,10,12,15,18,20,23,30,36,45,46,60,69,90,92,115,138,180,207,230,276,345,414,460,690,828,1035,1380,2070,4140
Greatest Common Factor
We found the factors 5880,4140 . The biggest common factor number is the GCF number.
So the greatest common factor 5880,4140 is 60.
Lets's calculate LCM of 205,1002
Given numbers has no common factors except 1. So, there LCM is their product i.e 205410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/205410
Therefore, the GCF of Fractions 5880/205,4140/1002 is 60/205410
Least Common Multiple of 205,1002 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 205,1002 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,1002) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,1002) x common factors =1 x 1 = 1
LCM(205,1002) = ( 205 × 1002 ) / 1
LCM(205,1002) = 205410 / 1
LCM(205,1002) = 205410
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FAQs on GCF of Fractions of 5880/205, 4140/1002
1. What is the HCF of 5880,4140?
The HCF of 5880,4140 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 5880/205, 4140/1002?
Answer: GCF of Numerators as per given numbers 5880/205, 4140/1002 is
GCF of Numerators i.e. for 5880,4140 is 60
LCM of denominators i.e. for 205,1002 is 205410.
Thus, GCF of Fractions is 60/205410.Finally, GCF of Fractions for 5880/205, 4140/1002 is 60/205410.