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GCF of 577/457, 217/978

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 577/457, 217/978 i.e 1/446946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 577/457, 217/978.

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 577/457,217/978?

Given fractions are 577/457,217/978

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 577/457,217/978, numerators are 577,217

Denominators are 457,978

The GCF of 577,217 is 1 .

LCM of 457,978 is 446946.

The greatest common factor of 577/457,217/978 = [GCF of 577,217]/[LCM of 457,978]= 1/446946

Therefore, the GCF of 577/457,217/978 is 1/446946.

Greatest Common Factor of 577,217

To find the highest common factor of 577,217, we have to find the factors of both numbers and list the highest common factor.

The factors of 577 are 1, 577

The factors of 217 are 1, 7, 31, 217

The HCF of 577,217 is 1.

Lets's calculate GCF of 577,217

Greatest Common Factor (GCF) of 577,217 By Common Division

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

Greatest Common Factor of 577,217 By Matching Biggest Common Factor Method

Greatest Common Factor of 577,217 By Matching Biggest Common Factor Method

Now, list down the factors of 577

:

1,577

Now, list down the factors of 217

:

1,7,31,217

Greatest Common Factor

We found the factors 577,217 . The biggest common factor number is the GCF number.
So the greatest common factor 577,217 is 1.

Lets's calculate LCM of 457,978

Lowest Common Multiple of 457,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 446946

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/446946

Therefore, the GCF of Fractions 577/457,217/978 is 1/446946

Least Common Multiple of 457,978 with GCF Formula

Least Common Multiple of 457,978 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 457,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(457,978) = 1

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

GCF(457,978) x common factors =1 x 1 = 1

LCM(457,978) = ( 457 × 978 ) / 1

LCM(457,978) = 446946 / 1

LCM(457,978) = 446946


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FAQs on GCF of Fractions of 577/457, 217/978

1. What is the HCF of 577,217?

The HCF of 577,217 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 577/457, 217/978?

Answer: GCF of Numerators as per given numbers 577/457, 217/978 is

GCF of Numerators i.e. for 577,217 is 1

LCM of denominators i.e. for 457,978 is 446946.

Thus, GCF of Fractions is 1/446946.Finally, GCF of Fractions for 577/457, 217/978 is 1/446946.