How to Find GCF of 6/17, 6/68, 9/55, 42/832?

GCF of 6/17, 6/68, 9/55, 42/832

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 6/17, 6/68, 9/55, 42/832 i.e 3/777920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/17, 6/68, 9/55, 42/832.

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 6/17,6/68,9/55,42/832?

Given fractions are 6/17,6/68,9/55,42/832

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 6/17,6/68,9/55,42/832, numerators are 6,6,9,42

Denominators are 17,68,55,832

The GCF of 6,6,9,42 is 3 .

LCM of 17,68,55,832 is 777920.

The greatest common factor of 6/17,6/68,9/55,42/832 = [GCF of 6,6,9,42]/[LCM of 17,68,55,832]= 3/777920

Therefore, the GCF of 6/17,6/68,9/55,42/832 is 3/777920.

Greatest Common Factor of 6,6,9,42

To find the highest common factor of 6,6,9,42, we have to find the factors of both numbers and list the highest common factor.

The factors of 6 are 1, 2, 3, 6

The factors of 9 are 1, 3, 9

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The HCF of 6,6,9,42 is 3.

Lets's calculate GCF of 6,6,9,42

Greatest Common Factor (GCF) of 6,6,9,42 By Common Division

3	6, 6, 9, 42
	2, 2, 3, 14

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 6,6,9,42 By Matching Biggest Common Factor Method

Now, list down the factors of 6

1,2,3,6

Now, list down the factors of 6

1,2,3,6

Now, list down the factors of 9

1,3,9

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Greatest Common Factor

We found the factors 6,6,9,42 . The biggest common factor number is the GCF number.
So the greatest common factor 6,6,9,42 is 3.

Lets's calculate LCM of 17,68,55,832

Lowest Common Multiple of 17,68,55,832 using Common Division

2	17, 68, 55, 832
2	17, 34, 55, 416
17	17, 17, 55, 208
	1, 1, 55, 208

∴ So the LCM of the given numbers is 2 x 2 x 17 x 1 x 1 x 55 x 208 = 777920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/777920

Therefore, the GCF of Fractions 6/17,6/68,9/55,42/832 is 3/777920

Least Common Multiple of 17,68,55,832 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 17,68,55,832 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,68,55,832) = 1

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

GCF(17,68,55,832) x common factors =1 x 68 = 68

LCM(17,68,55,832) = ( 17 × 68 × 55 × 832 ) / 68

LCM(17,68,55,832) = 52898560 / 68

LCM(17,68,55,832) = 777920

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 6/17, 6/68, 9/55, 42/832

1. What is the HCF of 6,6,9,42?

The HCF of 6,6,9,42 is 3

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 6/17, 6/68, 9/55, 42/832?

Answer: GCF of Numerators as per given numbers 6/17, 6/68, 9/55, 42/832 is

GCF of Numerators i.e. for 6,6,9,42 is 3

LCM of denominators i.e. for 17,68,55,832 is 777920.

Thus, GCF of Fractions is 3/777920.Finally, GCF of Fractions for 6/17, 6/68, 9/55, 42/832 is 3/777920.