How to Find GCF of 1755/360, 2300/442?

GCF of 1755/360, 2300/442

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 1755/360, 2300/442 i.e 5/79560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1755/360, 2300/442.

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 1755/360,2300/442?

Given fractions are 1755/360,2300/442

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 1755/360,2300/442, numerators are 1755,2300

Denominators are 360,442

The GCF of 1755,2300 is 5 .

LCM of 360,442 is 79560.

The greatest common factor of 1755/360,2300/442 = [GCF of 1755,2300]/[LCM of 360,442]= 5/79560

Therefore, the GCF of 1755/360,2300/442 is 5/79560.

Greatest Common Factor of 1755,2300

To find the highest common factor of 1755,2300, we have to find the factors of both numbers and list the highest common factor.

The factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755

The factors of 2300 are 1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150, 2300

The HCF of 1755,2300 is 5.

Lets's calculate GCF of 1755,2300

Greatest Common Factor (GCF) of 1755,2300 By Common Division

5	1755, 2300
	351, 460

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 1755,2300 By Matching Biggest Common Factor Method

Now, list down the factors of 1755

1,3,5,9,13,15,27,39,45,65,117,135,195,351,585,1755

Now, list down the factors of 2300

1,2,4,5,10,20,23,25,46,50,92,100,115,230,460,575,1150,2300

Greatest Common Factor

We found the factors 1755,2300 . The biggest common factor number is the GCF number.
So the greatest common factor 1755,2300 is 5.

Lets's calculate LCM of 360,442

Lowest Common Multiple of 360,442 using Common Division

2	360, 442
	180, 221

∴ So the LCM of the given numbers is 2 x 180 x 221 = 79560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/79560

Therefore, the GCF of Fractions 1755/360,2300/442 is 5/79560

Least Common Multiple of 360,442 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 360,442 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(360,442) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(360,442) x common factors =2 x 1 = 2

LCM(360,442) = ( 360 × 442 ) / 2

LCM(360,442) = 159120 / 2

LCM(360,442) = 79560

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FAQs on GCF of Fractions of 1755/360, 2300/442

1. What is the HCF of 1755,2300?

The HCF of 1755,2300 is 5

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 1755/360, 2300/442?

Answer: GCF of Numerators as per given numbers 1755/360, 2300/442 is

GCF of Numerators i.e. for 1755,2300 is 5

LCM of denominators i.e. for 360,442 is 79560.

Thus, GCF of Fractions is 5/79560.Finally, GCF of Fractions for 1755/360, 2300/442 is 5/79560.