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GCF of 196/17, 257/548

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 196/17, 257/548 i.e 1/9316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/17, 257/548.

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 196/17,257/548?

Given fractions are 196/17,257/548

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 196/17,257/548, numerators are 196,257

Denominators are 17,548

The GCF of 196,257 is 1 .

LCM of 17,548 is 9316.

The greatest common factor of 196/17,257/548 = [GCF of 196,257]/[LCM of 17,548]= 1/9316

Therefore, the GCF of 196/17,257/548 is 1/9316.

Greatest Common Factor of 196,257

To find the highest common factor of 196,257, we have to find the factors of both numbers and list the highest common factor.

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

The factors of 257 are 1, 257

The HCF of 196,257 is 1.

Lets's calculate GCF of 196,257

Greatest Common Factor (GCF) of 196,257 By Common Division

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

Greatest Common Factor of 196,257 By Matching Biggest Common Factor Method

Greatest Common Factor of 196,257 By Matching Biggest Common Factor Method

Now, list down the factors of 196

:

1,2,4,7,14,28,49,98,196

Now, list down the factors of 257

:

1,257

Greatest Common Factor

We found the factors 196,257 . The biggest common factor number is the GCF number.
So the greatest common factor 196,257 is 1.

Lets's calculate LCM of 17,548

Lowest Common Multiple of 17,548 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9316

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9316

Therefore, the GCF of Fractions 196/17,257/548 is 1/9316

Least Common Multiple of 17,548 with GCF Formula

Least Common Multiple of 17,548 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 17,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,548) = 1

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

GCF(17,548) x common factors =1 x 1 = 1

LCM(17,548) = ( 17 × 548 ) / 1

LCM(17,548) = 9316 / 1

LCM(17,548) = 9316


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 196/17, 257/548

1. What is the HCF of 196,257?

The HCF of 196,257 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 196/17, 257/548?

Answer: GCF of Numerators as per given numbers 196/17, 257/548 is

GCF of Numerators i.e. for 196,257 is 1

LCM of denominators i.e. for 17,548 is 9316.

Thus, GCF of Fractions is 1/9316.Finally, GCF of Fractions for 196/17, 257/548 is 1/9316.