How to Find GCF of 514/977, 4526/5178?

GCF of 514/977, 4526/5178

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 514/977, 4526/5178 i.e 2/5058906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/977, 4526/5178.

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 514/977,4526/5178?

Given fractions are 514/977,4526/5178

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 514/977,4526/5178, numerators are 514,4526

Denominators are 977,5178

The GCF of 514,4526 is 2 .

LCM of 977,5178 is 5058906.

The greatest common factor of 514/977,4526/5178 = [GCF of 514,4526]/[LCM of 977,5178]= 2/5058906

Therefore, the GCF of 514/977,4526/5178 is 2/5058906.

Greatest Common Factor of 514,4526

To find the highest common factor of 514,4526, we have to find the factors of both numbers and list the highest common factor.

The factors of 514 are 1, 2, 257, 514

The factors of 4526 are 1, 2, 31, 62, 73, 146, 2263, 4526

The HCF of 514,4526 is 2.

Lets's calculate GCF of 514,4526

Greatest Common Factor (GCF) of 514,4526 By Common Division

2	514, 4526
	257, 2263

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

Greatest Common Factor of 514,4526 By Matching Biggest Common Factor Method

Now, list down the factors of 514

1,2,257,514

Now, list down the factors of 4526

1,2,31,62,73,146,2263,4526

Greatest Common Factor

We found the factors 514,4526 . The biggest common factor number is the GCF number.
So the greatest common factor 514,4526 is 2.

Lets's calculate LCM of 977,5178

Lowest Common Multiple of 977,5178 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5058906

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5058906

Therefore, the GCF of Fractions 514/977,4526/5178 is 2/5058906

Least Common Multiple of 977,5178 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 977,5178 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(977,5178) = 1

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

GCF(977,5178) x common factors =1 x 1 = 1

LCM(977,5178) = ( 977 × 5178 ) / 1

LCM(977,5178) = 5058906 / 1

LCM(977,5178) = 5058906

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 514/977, 4526/5178

1. What is the HCF of 514,4526?

The HCF of 514,4526 is 2

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 514/977, 4526/5178?

Answer: GCF of Numerators as per given numbers 514/977, 4526/5178 is

GCF of Numerators i.e. for 514,4526 is 2

LCM of denominators i.e. for 977,5178 is 5058906.

Thus, GCF of Fractions is 2/5058906.Finally, GCF of Fractions for 514/977, 4526/5178 is 2/5058906.