How to Find GCF of 766/461, 1288/977?

GCF of 766/461, 1288/977

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 766/461, 1288/977 i.e 2/450397 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/461, 1288/977.

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 766/461,1288/977?

Given fractions are 766/461,1288/977

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 766/461,1288/977, numerators are 766,1288

Denominators are 461,977

The GCF of 766,1288 is 2 .

LCM of 461,977 is 450397.

The greatest common factor of 766/461,1288/977 = [GCF of 766,1288]/[LCM of 461,977]= 2/450397

Therefore, the GCF of 766/461,1288/977 is 2/450397.

Greatest Common Factor of 766,1288

To find the highest common factor of 766,1288, we have to find the factors of both numbers and list the highest common factor.

The factors of 766 are 1, 2, 383, 766

The factors of 1288 are 1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644, 1288

The HCF of 766,1288 is 2.

Lets's calculate GCF of 766,1288

Greatest Common Factor (GCF) of 766,1288 By Common Division

2	766, 1288
	383, 644

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

Greatest Common Factor of 766,1288 By Matching Biggest Common Factor Method

Now, list down the factors of 766

1,2,383,766

Now, list down the factors of 1288

1,2,4,7,8,14,23,28,46,56,92,161,184,322,644,1288

Greatest Common Factor

We found the factors 766,1288 . The biggest common factor number is the GCF number.
So the greatest common factor 766,1288 is 2.

Lets's calculate LCM of 461,977

Lowest Common Multiple of 461,977 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 450397

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/450397

Therefore, the GCF of Fractions 766/461,1288/977 is 2/450397

Least Common Multiple of 461,977 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 461,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(461,977) = 1

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

GCF(461,977) x common factors =1 x 1 = 1

LCM(461,977) = ( 461 × 977 ) / 1

LCM(461,977) = 450397 / 1

LCM(461,977) = 450397

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FAQs on GCF of Fractions of 766/461, 1288/977

1. What is the HCF of 766,1288?

The HCF of 766,1288 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 766/461, 1288/977?

Answer: GCF of Numerators as per given numbers 766/461, 1288/977 is

GCF of Numerators i.e. for 766,1288 is 2

LCM of denominators i.e. for 461,977 is 450397.

Thus, GCF of Fractions is 2/450397.Finally, GCF of Fractions for 766/461, 1288/977 is 2/450397.