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GCF of 977/512, 193/768

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 977/512, 193/768 i.e 1/1536 easily. The following is the detailed procedure to determine the greatest common factor of fractions 977/512, 193/768.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 977/512,193/768?

Given fractions are 977/512,193/768

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 977/512,193/768, numerators are 977,193

Denominators are 512,768

The GCF of 977,193 is 1 .

LCM of 512,768 is 1536.

The greatest common factor of 977/512,193/768 = [GCF of 977,193]/[LCM of 512,768]= 1/1536

Therefore, the GCF of 977/512,193/768 is 1/1536.

Greatest Common Factor of 977,193

To find the highest common factor of 977,193, we have to find the factors of both numbers and list the highest common factor.

The factors of 977 are 1, 977

The factors of 193 are 1, 193

The HCF of 977,193 is 1.

Lets's calculate GCF of 977,193

Greatest Common Factor (GCF) of 977,193 By Common Division

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

Greatest Common Factor of 977,193 By Matching Biggest Common Factor Method

Greatest Common Factor of 977,193 By Matching Biggest Common Factor Method

Now, list down the factors of 977

:

1,977

Now, list down the factors of 193

:

1,193

Greatest Common Factor

We found the factors 977,193 . The biggest common factor number is the GCF number.
So the greatest common factor 977,193 is 1.

Lets's calculate LCM of 512,768

Lowest Common Multiple of 512,768 using Common Division

2 512, 768
2 256, 384
2 128, 192
2 64, 96
2 32, 48
2 16, 24
2 8, 12
2 4, 6
2, 3

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 1536

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1536

Therefore, the GCF of Fractions 977/512,193/768 is 1/1536

Least Common Multiple of 512,768 with GCF Formula

Least Common Multiple of 512,768 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 512,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(512,768) = 256

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

GCF(512,768) x common factors =256 x 1 = 256

LCM(512,768) = ( 512 × 768 ) / 256

LCM(512,768) = 393216 / 256

LCM(512,768) = 1536


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FAQs on GCF of Fractions of 977/512, 193/768

1. What is the HCF of 977,193?

The HCF of 977,193 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 977/512, 193/768?

Answer: GCF of Numerators as per given numbers 977/512, 193/768 is

GCF of Numerators i.e. for 977,193 is 1

LCM of denominators i.e. for 512,768 is 1536.

Thus, GCF of Fractions is 1/1536.Finally, GCF of Fractions for 977/512, 193/768 is 1/1536.