How to Find GCF of 646/776, 689/697?

GCF of 646/776, 689/697

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 646/776, 689/697 i.e 1/540872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/776, 689/697.

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 646/776,689/697?

Given fractions are 646/776,689/697

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 646/776,689/697, numerators are 646,689

Denominators are 776,697

The GCF of 646,689 is 1 .

LCM of 776,697 is 540872.

The greatest common factor of 646/776,689/697 = [GCF of 646,689]/[LCM of 776,697]= 1/540872

Therefore, the GCF of 646/776,689/697 is 1/540872.

Greatest Common Factor of 646,689

To find the highest common factor of 646,689, we have to find the factors of both numbers and list the highest common factor.

The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646

The factors of 689 are 1, 13, 53, 689

The HCF of 646,689 is 1.

Lets's calculate GCF of 646,689

Greatest Common Factor (GCF) of 646,689 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 646,689 By Matching Biggest Common Factor Method

Now, list down the factors of 646

1,2,17,19,34,38,323,646

Now, list down the factors of 689

1,13,53,689

Greatest Common Factor

We found the factors 646,689 . The biggest common factor number is the GCF number.
So the greatest common factor 646,689 is 1.

Lets's calculate LCM of 776,697

Lowest Common Multiple of 776,697 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 540872

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/540872

Therefore, the GCF of Fractions 646/776,689/697 is 1/540872

Least Common Multiple of 776,697 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 776,697 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(776,697) = 1

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

GCF(776,697) x common factors =1 x 1 = 1

LCM(776,697) = ( 776 × 697 ) / 1

LCM(776,697) = 540872 / 1

LCM(776,697) = 540872

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FAQs on GCF of Fractions of 646/776, 689/697

1. What is the HCF of 646,689?

The HCF of 646,689 is 1

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 646/776, 689/697?

Answer: GCF of Numerators as per given numbers 646/776, 689/697 is

GCF of Numerators i.e. for 646,689 is 1

LCM of denominators i.e. for 776,697 is 540872.

Thus, GCF of Fractions is 1/540872.Finally, GCF of Fractions for 646/776, 689/697 is 1/540872.