How to Find GCF of 58/89, 64/69, 200/35?

GCF of 58/89, 64/69, 200/35

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 58/89, 64/69, 200/35 i.e 2/214935 easily. The following is the detailed procedure to determine the greatest common factor of fractions 58/89, 64/69, 200/35.

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 58/89,64/69,200/35?

Given fractions are 58/89,64/69,200/35

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 58/89,64/69,200/35, numerators are 58,64,200

Denominators are 89,69,35

The GCF of 58,64,200 is 2 .

LCM of 89,69,35 is 214935.

The greatest common factor of 58/89,64/69,200/35 = [GCF of 58,64,200]/[LCM of 89,69,35]= 2/214935

Therefore, the GCF of 58/89,64/69,200/35 is 2/214935.

Greatest Common Factor of 58,64,200

To find the highest common factor of 58,64,200, we have to find the factors of both numbers and list the highest common factor.

The factors of 58 are 1, 2, 29, 58

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

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The HCF of 58,64,200 is 2.

Lets's calculate GCF of 58,64,200

Greatest Common Factor (GCF) of 58,64,200 By Common Division

2	58, 64, 200
	29, 32, 100

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

Greatest Common Factor of 58,64,200 By Matching Biggest Common Factor Method

Now, list down the factors of 58

1,2,29,58

Now, list down the factors of 64

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

Now, list down the factors of 200

1,2,4,5,8,10,20,25,40,50,100,200

Greatest Common Factor

We found the factors 58,64,200 . The biggest common factor number is the GCF number.
So the greatest common factor 58,64,200 is 2.

Lets's calculate LCM of 89,69,35

Lowest Common Multiple of 89,69,35 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 214935

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/214935

Therefore, the GCF of Fractions 58/89,64/69,200/35 is 2/214935

Least Common Multiple of 89,69,35 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 89,69,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(89,69,35) = 1

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

GCF(89,69,35) x common factors =1 x 1 = 1

LCM(89,69,35) = ( 89 × 69 × 35 ) / 1

LCM(89,69,35) = 214935 / 1

LCM(89,69,35) = 214935

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FAQs on GCF of Fractions of 58/89, 64/69, 200/35

1. What is the HCF of 58,64,200?

The HCF of 58,64,200 is 2

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 58/89, 64/69, 200/35?

Answer: GCF of Numerators as per given numbers 58/89, 64/69, 200/35 is

GCF of Numerators i.e. for 58,64,200 is 2

LCM of denominators i.e. for 89,69,35 is 214935.

Thus, GCF of Fractions is 2/214935.Finally, GCF of Fractions for 58/89, 64/69, 200/35 is 2/214935.