How to Find GCF of 180/480, 4216/345?

GCF of 180/480, 4216/345

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 180/480, 4216/345 i.e 4/11040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/480, 4216/345.

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 180/480,4216/345?

Given fractions are 180/480,4216/345

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 180/480,4216/345, numerators are 180,4216

Denominators are 480,345

The GCF of 180,4216 is 4 .

LCM of 480,345 is 11040.

The greatest common factor of 180/480,4216/345 = [GCF of 180,4216]/[LCM of 480,345]= 4/11040

Therefore, the GCF of 180/480,4216/345 is 4/11040.

Greatest Common Factor of 180,4216

To find the highest common factor of 180,4216, we have to find the factors of both numbers and list the highest common factor.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 4216 are 1, 2, 4, 8, 17, 31, 34, 62, 68, 124, 136, 248, 527, 1054, 2108, 4216

The HCF of 180,4216 is 4.

Lets's calculate GCF of 180,4216

Greatest Common Factor (GCF) of 180,4216 By Common Division

2	180, 4216
2	90, 2108
	45, 1054

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 180,4216 By Matching Biggest Common Factor Method

Now, list down the factors of 180

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Now, list down the factors of 4216

1,2,4,8,17,31,34,62,68,124,136,248,527,1054,2108,4216

Greatest Common Factor

We found the factors 180,4216 . The biggest common factor number is the GCF number.
So the greatest common factor 180,4216 is 4.

Lets's calculate LCM of 480,345

Lowest Common Multiple of 480,345 using Common Division

3	480, 345
5	160, 115
	32, 23

∴ So the LCM of the given numbers is 3 x 5 x 32 x 23 = 11040

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/11040

Therefore, the GCF of Fractions 180/480,4216/345 is 4/11040

Least Common Multiple of 480,345 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 480,345 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(480,345) = 15

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

GCF(480,345) x common factors =15 x 1 = 15

LCM(480,345) = ( 480 × 345 ) / 15

LCM(480,345) = 165600 / 15

LCM(480,345) = 11040

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FAQs on GCF of Fractions of 180/480, 4216/345

1. What is the HCF of 180,4216?

The HCF of 180,4216 is 4

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 180/480, 4216/345?

Answer: GCF of Numerators as per given numbers 180/480, 4216/345 is

GCF of Numerators i.e. for 180,4216 is 4

LCM of denominators i.e. for 480,345 is 11040.

Thus, GCF of Fractions is 4/11040.Finally, GCF of Fractions for 180/480, 4216/345 is 4/11040.