How to Find GCF of 175/42, 169/89, 909/82?

GCF of 175/42, 169/89, 909/82

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 175/42, 169/89, 909/82 i.e 1/153258 easily. The following is the detailed procedure to determine the greatest common factor of fractions 175/42, 169/89, 909/82.

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 175/42,169/89,909/82?

Given fractions are 175/42,169/89,909/82

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 175/42,169/89,909/82, numerators are 175,169,909

Denominators are 42,89,82

The GCF of 175,169,909 is 1 .

LCM of 42,89,82 is 153258.

The greatest common factor of 175/42,169/89,909/82 = [GCF of 175,169,909]/[LCM of 42,89,82]= 1/153258

Therefore, the GCF of 175/42,169/89,909/82 is 1/153258.

Greatest Common Factor of 175,169,909

To find the highest common factor of 175,169,909, we have to find the factors of both numbers and list the highest common factor.

The factors of 175 are 1, 5, 7, 25, 35, 175

The factors of 169 are 1, 13, 169

The factors of 909 are 1, 3, 9, 101, 303, 909

The HCF of 175,169,909 is 1.

Lets's calculate GCF of 175,169,909

Greatest Common Factor (GCF) of 175,169,909 By Common Division

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

Greatest Common Factor of 175,169,909 By Matching Biggest Common Factor Method

Now, list down the factors of 175

1,5,7,25,35,175

Now, list down the factors of 169

1,13,169

Now, list down the factors of 909

1,3,9,101,303,909

Greatest Common Factor

We found the factors 175,169,909 . The biggest common factor number is the GCF number.
So the greatest common factor 175,169,909 is 1.

Lets's calculate LCM of 42,89,82

Lowest Common Multiple of 42,89,82 using Common Division

2	42, 89, 82
	21, 89, 41

∴ So the LCM of the given numbers is 2 x 21 x 89 x 41 = 153258

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/153258

Therefore, the GCF of Fractions 175/42,169/89,909/82 is 1/153258

Least Common Multiple of 42,89,82 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 42,89,82 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,89,82) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(42,89,82) x common factors =1 x 2 = 2

LCM(42,89,82) = ( 42 × 89 × 82 ) / 2

LCM(42,89,82) = 306516 / 2

LCM(42,89,82) = 153258

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FAQs on GCF of Fractions of 175/42, 169/89, 909/82

1. What is the HCF of 175,169,909?

The HCF of 175,169,909 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 175/42, 169/89, 909/82?

Answer: GCF of Numerators as per given numbers 175/42, 169/89, 909/82 is

GCF of Numerators i.e. for 175,169,909 is 1

LCM of denominators i.e. for 42,89,82 is 153258.

Thus, GCF of Fractions is 1/153258.Finally, GCF of Fractions for 175/42, 169/89, 909/82 is 1/153258.