GCF of 2145/714, 4180/2580
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2145/714, 4180/2580 i.e 55/307020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2145/714, 4180/2580.
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 2145/714,4180/2580?
Given fractions are 2145/714,4180/2580
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 2145/714,4180/2580, numerators are 2145,4180
Denominators are 714,2580
The GCF of 2145,4180 is 55 .
LCM of 714,2580 is 307020.
The greatest common factor of 2145/714,4180/2580 = [GCF of 2145,4180]/[LCM of 714,2580]= 55/307020
Therefore, the GCF of 2145/714,4180/2580 is 55/307020.
To find the highest common factor of 2145,4180, we have to find the factors of both numbers and list the highest common factor.
The factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145
The factors of 4180 are 1, 2, 4, 5, 10, 11, 19, 20, 22, 38, 44, 55, 76, 95, 110, 190, 209, 220, 380, 418, 836, 1045, 2090, 4180
The HCF of 2145,4180 is 55.
Lets's calculate GCF of 2145,4180
| 5 | 2145, 4180 |
| 11 | 429, 836 |
| 39, 76 |
∴ So the GCF of the given numbers is 5 x 11 = 55
Greatest Common Factor of 2145,4180 By Matching Biggest Common Factor Method
Now, list down the factors of 2145
:1,3,5,11,13,15,33,39,55,65,143,165,195,429,715,2145
Now, list down the factors of 4180
:1,2,4,5,10,11,19,20,22,38,44,55,76,95,110,190,209,220,380,418,836,1045,2090,4180
Greatest Common Factor
We found the factors 2145,4180 . The biggest common factor number is the GCF number.
So the greatest common factor 2145,4180 is 55.
Lets's calculate LCM of 714,2580
| 2 | 714, 2580 |
| 3 | 357, 1290 |
| 119, 430 |
∴ So the LCM of the given numbers is 2 x 3 x 119 x 430 = 307020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 55/307020
Therefore, the GCF of Fractions 2145/714,4180/2580 is 55/307020
Least Common Multiple of 714,2580 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 714,2580 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(714,2580) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(714,2580) x common factors =6 x 1 = 6
LCM(714,2580) = ( 714 × 2580 ) / 6
LCM(714,2580) = 1842120 / 6
LCM(714,2580) = 307020
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FAQs on GCF of Fractions of 2145/714, 4180/2580
1. What is the HCF of 2145,4180?
The HCF of 2145,4180 is 55
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 2145/714, 4180/2580?
Answer: GCF of Numerators as per given numbers 2145/714, 4180/2580 is
GCF of Numerators i.e. for 2145,4180 is 55
LCM of denominators i.e. for 714,2580 is 307020.
Thus, GCF of Fractions is 55/307020.Finally, GCF of Fractions for 2145/714, 4180/2580 is 55/307020.