How to Find GCF of 23/76, 64/40, 198/69?

GCF of 23/76, 64/40, 198/69

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 23/76, 64/40, 198/69 i.e 1/52440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/76, 64/40, 198/69.

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 23/76,64/40,198/69?

Given fractions are 23/76,64/40,198/69

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 23/76,64/40,198/69, numerators are 23,64,198

Denominators are 76,40,69

The GCF of 23,64,198 is 1 .

LCM of 76,40,69 is 52440.

The greatest common factor of 23/76,64/40,198/69 = [GCF of 23,64,198]/[LCM of 76,40,69]= 1/52440

Therefore, the GCF of 23/76,64/40,198/69 is 1/52440.

Greatest Common Factor of 23,64,198

To find the highest common factor of 23,64,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 23 are 1, 23

The factors of 64 are 1, 2, 4, 8, 16, 32, 64

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 23,64,198 is 1.

Lets's calculate GCF of 23,64,198

Greatest Common Factor (GCF) of 23,64,198 By Common Division

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

Greatest Common Factor of 23,64,198 By Matching Biggest Common Factor Method

Now, list down the factors of 23

1,23

Now, list down the factors of 64

1,2,4,8,16,32,64

Now, list down the factors of 198

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 23,64,198 . The biggest common factor number is the GCF number.
So the greatest common factor 23,64,198 is 1.

Lets's calculate LCM of 76,40,69

Lowest Common Multiple of 76,40,69 using Common Division

2	76, 40, 69
2	38, 20, 69
	19, 10, 69

∴ So the LCM of the given numbers is 2 x 2 x 19 x 10 x 69 = 52440

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/52440

Therefore, the GCF of Fractions 23/76,64/40,198/69 is 1/52440

Least Common Multiple of 76,40,69 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 76,40,69 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,40,69) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(76,40,69) x common factors =1 x 4 = 4

LCM(76,40,69) = ( 76 × 40 × 69 ) / 4

LCM(76,40,69) = 209760 / 4

LCM(76,40,69) = 52440

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FAQs on GCF of Fractions of 23/76, 64/40, 198/69

1. What is the HCF of 23,64,198?

The HCF of 23,64,198 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 23/76, 64/40, 198/69?

Answer: GCF of Numerators as per given numbers 23/76, 64/40, 198/69 is

GCF of Numerators i.e. for 23,64,198 is 1

LCM of denominators i.e. for 76,40,69 is 52440.

Thus, GCF of Fractions is 1/52440.Finally, GCF of Fractions for 23/76, 64/40, 198/69 is 1/52440.