How to Find GCF of 561/412, 770/556?

GCF of 561/412, 770/556

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 561/412, 770/556 i.e 11/57268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 561/412, 770/556.

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 561/412,770/556?

Given fractions are 561/412,770/556

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 561/412,770/556, numerators are 561,770

Denominators are 412,556

The GCF of 561,770 is 11 .

LCM of 412,556 is 57268.

The greatest common factor of 561/412,770/556 = [GCF of 561,770]/[LCM of 412,556]= 11/57268

Therefore, the GCF of 561/412,770/556 is 11/57268.

Greatest Common Factor of 561,770

To find the highest common factor of 561,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 561,770 is 11.

Lets's calculate GCF of 561,770

Greatest Common Factor (GCF) of 561,770 By Common Division

11	561, 770
	51, 70

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 561,770 By Matching Biggest Common Factor Method

Now, list down the factors of 561

1,3,11,17,33,51,187,561

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 561,770 . The biggest common factor number is the GCF number.
So the greatest common factor 561,770 is 11.

Lets's calculate LCM of 412,556

Lowest Common Multiple of 412,556 using Common Division

2	412, 556
2	206, 278
	103, 139

∴ So the LCM of the given numbers is 2 x 2 x 103 x 139 = 57268

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/57268

Therefore, the GCF of Fractions 561/412,770/556 is 11/57268

Least Common Multiple of 412,556 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 412,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(412,556) = 4

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

GCF(412,556) x common factors =4 x 1 = 4

LCM(412,556) = ( 412 × 556 ) / 4

LCM(412,556) = 229072 / 4

LCM(412,556) = 57268

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FAQs on GCF of Fractions of 561/412, 770/556

1. What is the HCF of 561,770?

The HCF of 561,770 is 11

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 561/412, 770/556?

Answer: GCF of Numerators as per given numbers 561/412, 770/556 is

GCF of Numerators i.e. for 561,770 is 11

LCM of denominators i.e. for 412,556 is 57268.

Thus, GCF of Fractions is 11/57268.Finally, GCF of Fractions for 561/412, 770/556 is 11/57268.