How to Find GCF of 19/122, 45/832, 189/258?

GCF of 19/122, 45/832, 189/258

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 19/122, 45/832, 189/258 i.e 1/6547008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/122, 45/832, 189/258.

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 19/122,45/832,189/258?

Given fractions are 19/122,45/832,189/258

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 19/122,45/832,189/258, numerators are 19,45,189

Denominators are 122,832,258

The GCF of 19,45,189 is 1 .

LCM of 122,832,258 is 6547008.

The greatest common factor of 19/122,45/832,189/258 = [GCF of 19,45,189]/[LCM of 122,832,258]= 1/6547008

Therefore, the GCF of 19/122,45/832,189/258 is 1/6547008.

Greatest Common Factor of 19,45,189

To find the highest common factor of 19,45,189, we have to find the factors of both numbers and list the highest common factor.

The factors of 19 are 1, 19

The factors of 45 are 1, 3, 5, 9, 15, 45

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The HCF of 19,45,189 is 1.

Lets's calculate GCF of 19,45,189

Greatest Common Factor (GCF) of 19,45,189 By Common Division

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

Greatest Common Factor of 19,45,189 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 45

1,3,5,9,15,45

Now, list down the factors of 189

1,3,7,9,21,27,63,189

Greatest Common Factor

We found the factors 19,45,189 . The biggest common factor number is the GCF number.
So the greatest common factor 19,45,189 is 1.

Lets's calculate LCM of 122,832,258

Lowest Common Multiple of 122,832,258 using Common Division

2	122, 832, 258
	61, 416, 129

∴ So the LCM of the given numbers is 2 x 61 x 416 x 129 = 6547008

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6547008

Therefore, the GCF of Fractions 19/122,45/832,189/258 is 1/6547008

Least Common Multiple of 122,832,258 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 122,832,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(122,832,258) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(122,832,258) x common factors =2 x 2 = 4

LCM(122,832,258) = ( 122 × 832 × 258 ) / 4

LCM(122,832,258) = 26188032 / 4

LCM(122,832,258) = 6547008

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FAQs on GCF of Fractions of 19/122, 45/832, 189/258

1. What is the HCF of 19,45,189?

The HCF of 19,45,189 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 19/122, 45/832, 189/258?

Answer: GCF of Numerators as per given numbers 19/122, 45/832, 189/258 is

GCF of Numerators i.e. for 19,45,189 is 1

LCM of denominators i.e. for 122,832,258 is 6547008.

Thus, GCF of Fractions is 1/6547008.Finally, GCF of Fractions for 19/122, 45/832, 189/258 is 1/6547008.