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GCF of 196/54, 584/419

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 196/54, 584/419 i.e 4/22626 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/54, 584/419.

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 196/54,584/419?

Given fractions are 196/54,584/419

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 196/54,584/419, numerators are 196,584

Denominators are 54,419

The GCF of 196,584 is 4 .

LCM of 54,419 is 22626.

The greatest common factor of 196/54,584/419 = [GCF of 196,584]/[LCM of 54,419]= 4/22626

Therefore, the GCF of 196/54,584/419 is 4/22626.

Greatest Common Factor of 196,584

To find the highest common factor of 196,584, 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 584 are 1, 2, 4, 8, 73, 146, 292, 584

The HCF of 196,584 is 4.

Lets's calculate GCF of 196,584

Greatest Common Factor (GCF) of 196,584 By Common Division

2 196, 584
2 98, 292
49, 146

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 196,584 By Matching Biggest Common Factor Method

Greatest Common Factor of 196,584 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 584

:

1,2,4,8,73,146,292,584

Greatest Common Factor

We found the factors 196,584 . The biggest common factor number is the GCF number.
So the greatest common factor 196,584 is 4.

Lets's calculate LCM of 54,419

Lowest Common Multiple of 54,419 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 22626

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/22626

Therefore, the GCF of Fractions 196/54,584/419 is 4/22626

Least Common Multiple of 54,419 with GCF Formula

Least Common Multiple of 54,419 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 54,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,419) = 1

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

GCF(54,419) x common factors =1 x 1 = 1

LCM(54,419) = ( 54 × 419 ) / 1

LCM(54,419) = 22626 / 1

LCM(54,419) = 22626


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FAQs on GCF of Fractions of 196/54, 584/419

1. What is the HCF of 196,584?

The HCF of 196,584 is 4

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 196/54, 584/419?

Answer: GCF of Numerators as per given numbers 196/54, 584/419 is

GCF of Numerators i.e. for 196,584 is 4

LCM of denominators i.e. for 54,419 is 22626.

Thus, GCF of Fractions is 4/22626.Finally, GCF of Fractions for 196/54, 584/419 is 4/22626.