How to Find GCF of 27/680, 95/916, 200/748?

GCF of 27/680, 95/916, 200/748

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 27/680, 95/916, 200/748 i.e 1/1712920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/680, 95/916, 200/748.

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 27/680,95/916,200/748?

Given fractions are 27/680,95/916,200/748

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 27/680,95/916,200/748, numerators are 27,95,200

Denominators are 680,916,748

The GCF of 27,95,200 is 1 .

LCM of 680,916,748 is 1712920.

The greatest common factor of 27/680,95/916,200/748 = [GCF of 27,95,200]/[LCM of 680,916,748]= 1/1712920

Therefore, the GCF of 27/680,95/916,200/748 is 1/1712920.

Greatest Common Factor of 27,95,200

To find the highest common factor of 27,95,200, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 95 are 1, 5, 19, 95

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

The HCF of 27,95,200 is 1.

Lets's calculate GCF of 27,95,200

Greatest Common Factor (GCF) of 27,95,200 By Common Division

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

Greatest Common Factor of 27,95,200 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 95

1,5,19,95

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 27,95,200 . The biggest common factor number is the GCF number.
So the greatest common factor 27,95,200 is 1.

Lets's calculate LCM of 680,916,748

Lowest Common Multiple of 680,916,748 using Common Division

2	680, 916, 748
2	340, 458, 374
17	170, 229, 187
	10, 229, 11

∴ So the LCM of the given numbers is 2 x 2 x 17 x 10 x 229 x 11 = 1712920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1712920

Therefore, the GCF of Fractions 27/680,95/916,200/748 is 1/1712920

Least Common Multiple of 680,916,748 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 680,916,748 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(680,916,748) = 4

common factors(in case of two or more numbers have common factors) = 68

GCF(680,916,748) x common factors =4 x 68 = 272

LCM(680,916,748) = ( 680 × 916 × 748 ) / 272

LCM(680,916,748) = 465914240 / 272

LCM(680,916,748) = 1712920

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 27/680, 95/916, 200/748

1. What is the HCF of 27,95,200?

The HCF of 27,95,200 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 27/680, 95/916, 200/748?

Answer: GCF of Numerators as per given numbers 27/680, 95/916, 200/748 is

GCF of Numerators i.e. for 27,95,200 is 1

LCM of denominators i.e. for 680,916,748 is 1712920.

Thus, GCF of Fractions is 1/1712920.Finally, GCF of Fractions for 27/680, 95/916, 200/748 is 1/1712920.