How to Find GCF of 143/180, 5161/1546?

GCF of 143/180, 5161/1546

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 143/180, 5161/1546 i.e 13/139140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 143/180, 5161/1546.

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 143/180,5161/1546?

Given fractions are 143/180,5161/1546

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 143/180,5161/1546, numerators are 143,5161

Denominators are 180,1546

The GCF of 143,5161 is 13 .

LCM of 180,1546 is 139140.

The greatest common factor of 143/180,5161/1546 = [GCF of 143,5161]/[LCM of 180,1546]= 13/139140

Therefore, the GCF of 143/180,5161/1546 is 13/139140.

Greatest Common Factor of 143,5161

To find the highest common factor of 143,5161, we have to find the factors of both numbers and list the highest common factor.

The factors of 143 are 1, 11, 13, 143

The factors of 5161 are 1, 13, 397, 5161

The HCF of 143,5161 is 13.

Lets's calculate GCF of 143,5161

Greatest Common Factor (GCF) of 143,5161 By Common Division

13	143, 5161
	11, 397

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 143,5161 By Matching Biggest Common Factor Method

Now, list down the factors of 143

1,11,13,143

Now, list down the factors of 5161

1,13,397,5161

Greatest Common Factor

We found the factors 143,5161 . The biggest common factor number is the GCF number.
So the greatest common factor 143,5161 is 13.

Lets's calculate LCM of 180,1546

Lowest Common Multiple of 180,1546 using Common Division

2	180, 1546
	90, 773

∴ So the LCM of the given numbers is 2 x 90 x 773 = 139140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/139140

Therefore, the GCF of Fractions 143/180,5161/1546 is 13/139140

Least Common Multiple of 180,1546 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 180,1546 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(180,1546) = 2

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

GCF(180,1546) x common factors =2 x 1 = 2

LCM(180,1546) = ( 180 × 1546 ) / 2

LCM(180,1546) = 278280 / 2

LCM(180,1546) = 139140

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FAQs on GCF of Fractions of 143/180, 5161/1546

1. What is the HCF of 143,5161?

The HCF of 143,5161 is 13

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 143/180, 5161/1546?

Answer: GCF of Numerators as per given numbers 143/180, 5161/1546 is

GCF of Numerators i.e. for 143,5161 is 13

LCM of denominators i.e. for 180,1546 is 139140.

Thus, GCF of Fractions is 13/139140.Finally, GCF of Fractions for 143/180, 5161/1546 is 13/139140.