How to Find GCF of 30/168, 65/776, 205/445?

GCF of 30/168, 65/776, 205/445

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 30/168, 65/776, 205/445 i.e 5/7251720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/168, 65/776, 205/445.

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 30/168,65/776,205/445?

Given fractions are 30/168,65/776,205/445

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 30/168,65/776,205/445, numerators are 30,65,205

Denominators are 168,776,445

The GCF of 30,65,205 is 5 .

LCM of 168,776,445 is 7251720.

The greatest common factor of 30/168,65/776,205/445 = [GCF of 30,65,205]/[LCM of 168,776,445]= 5/7251720

Therefore, the GCF of 30/168,65/776,205/445 is 5/7251720.

Greatest Common Factor of 30,65,205

To find the highest common factor of 30,65,205, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 65 are 1, 5, 13, 65

The factors of 205 are 1, 5, 41, 205

The HCF of 30,65,205 is 5.

Lets's calculate GCF of 30,65,205

Greatest Common Factor (GCF) of 30,65,205 By Common Division

5	30, 65, 205
	6, 13, 41

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 30,65,205 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 205

1,5,41,205

Greatest Common Factor

We found the factors 30,65,205 . The biggest common factor number is the GCF number.
So the greatest common factor 30,65,205 is 5.

Lets's calculate LCM of 168,776,445

Lowest Common Multiple of 168,776,445 using Common Division

2	168, 776, 445
2	84, 388, 445
2	42, 194, 445
	21, 97, 445

∴ So the LCM of the given numbers is 2 x 2 x 2 x 21 x 97 x 445 = 7251720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/7251720

Therefore, the GCF of Fractions 30/168,65/776,205/445 is 5/7251720

Least Common Multiple of 168,776,445 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 168,776,445 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(168,776,445) = 1

common factors(in case of two or more numbers have common factors) = 8

GCF(168,776,445) x common factors =1 x 8 = 8

LCM(168,776,445) = ( 168 × 776 × 445 ) / 8

LCM(168,776,445) = 58013760 / 8

LCM(168,776,445) = 7251720

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/168, 65/776, 205/445

1. What is the HCF of 30,65,205?

The HCF of 30,65,205 is 5

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 30/168, 65/776, 205/445?

Answer: GCF of Numerators as per given numbers 30/168, 65/776, 205/445 is

GCF of Numerators i.e. for 30,65,205 is 5

LCM of denominators i.e. for 168,776,445 is 7251720.

Thus, GCF of Fractions is 5/7251720.Finally, GCF of Fractions for 30/168, 65/776, 205/445 is 5/7251720.