How to Find GCF of 360/380, 520/298?

GCF of 360/380, 520/298

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 360/380, 520/298 i.e 40/56620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/380, 520/298.

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 360/380,520/298?

Given fractions are 360/380,520/298

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 360/380,520/298, numerators are 360,520

Denominators are 380,298

The GCF of 360,520 is 40 .

LCM of 380,298 is 56620.

The greatest common factor of 360/380,520/298 = [GCF of 360,520]/[LCM of 380,298]= 40/56620

Therefore, the GCF of 360/380,520/298 is 40/56620.

Greatest Common Factor of 360,520

To find the highest common factor of 360,520, we have to find the factors of both numbers and list the highest common factor.

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

The HCF of 360,520 is 40.

Lets's calculate GCF of 360,520

Greatest Common Factor (GCF) of 360,520 By Common Division

2	360, 520
2	180, 260
2	90, 130
5	45, 65
	9, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 360,520 By Matching Biggest Common Factor Method

Now, list down the factors of 360

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Now, list down the factors of 520

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Greatest Common Factor

We found the factors 360,520 . The biggest common factor number is the GCF number.
So the greatest common factor 360,520 is 40.

Lets's calculate LCM of 380,298

Lowest Common Multiple of 380,298 using Common Division

2	380, 298
	190, 149

∴ So the LCM of the given numbers is 2 x 190 x 149 = 56620

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/56620

Therefore, the GCF of Fractions 360/380,520/298 is 40/56620

Least Common Multiple of 380,298 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 380,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(380,298) = 2

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

GCF(380,298) x common factors =2 x 1 = 2

LCM(380,298) = ( 380 × 298 ) / 2

LCM(380,298) = 113240 / 2

LCM(380,298) = 56620

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FAQs on GCF of Fractions of 360/380, 520/298

1. What is the HCF of 360,520?

The HCF of 360,520 is 40

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 360/380, 520/298?

Answer: GCF of Numerators as per given numbers 360/380, 520/298 is

GCF of Numerators i.e. for 360,520 is 40

LCM of denominators i.e. for 380,298 is 56620.

Thus, GCF of Fractions is 40/56620.Finally, GCF of Fractions for 360/380, 520/298 is 40/56620.