How to Find GCF of 57/68, 998/82, 169/765?

GCF of 57/68, 998/82, 169/765

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 57/68, 998/82, 169/765 i.e 1/125460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 57/68, 998/82, 169/765.

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 57/68,998/82,169/765?

Given fractions are 57/68,998/82,169/765

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 57/68,998/82,169/765, numerators are 57,998,169

Denominators are 68,82,765

The GCF of 57,998,169 is 1 .

LCM of 68,82,765 is 125460.

The greatest common factor of 57/68,998/82,169/765 = [GCF of 57,998,169]/[LCM of 68,82,765]= 1/125460

Therefore, the GCF of 57/68,998/82,169/765 is 1/125460.

Greatest Common Factor of 57,998,169

To find the highest common factor of 57,998,169, we have to find the factors of both numbers and list the highest common factor.

The factors of 57 are 1, 3, 19, 57

The factors of 998 are 1, 2, 499, 998

The factors of 169 are 1, 13, 169

The HCF of 57,998,169 is 1.

Lets's calculate GCF of 57,998,169

Greatest Common Factor (GCF) of 57,998,169 By Common Division

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

Greatest Common Factor of 57,998,169 By Matching Biggest Common Factor Method

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 998

1,2,499,998

Now, list down the factors of 169

1,13,169

Greatest Common Factor

We found the factors 57,998,169 . The biggest common factor number is the GCF number.
So the greatest common factor 57,998,169 is 1.

Lets's calculate LCM of 68,82,765

Lowest Common Multiple of 68,82,765 using Common Division

2	68, 82, 765
17	34, 41, 765
	2, 41, 45

∴ So the LCM of the given numbers is 2 x 17 x 2 x 41 x 45 = 125460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/125460

Therefore, the GCF of Fractions 57/68,998/82,169/765 is 1/125460

Least Common Multiple of 68,82,765 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 68,82,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,82,765) = 1

common factors(in case of two or more numbers have common factors) = 34

GCF(68,82,765) x common factors =1 x 34 = 34

LCM(68,82,765) = ( 68 × 82 × 765 ) / 34

LCM(68,82,765) = 4265640 / 34

LCM(68,82,765) = 125460

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 57/68, 998/82, 169/765

1. What is the HCF of 57,998,169?

The HCF of 57,998,169 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 57/68, 998/82, 169/765?

Answer: GCF of Numerators as per given numbers 57/68, 998/82, 169/765 is

GCF of Numerators i.e. for 57,998,169 is 1

LCM of denominators i.e. for 68,82,765 is 125460.

Thus, GCF of Fractions is 1/125460.Finally, GCF of Fractions for 57/68, 998/82, 169/765 is 1/125460.