How to Find GCF of 31/176, 969/285, 921/638?

GCF of 31/176, 969/285, 921/638

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 31/176, 969/285, 921/638 i.e 1/1454640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/176, 969/285, 921/638.

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 31/176,969/285,921/638?

Given fractions are 31/176,969/285,921/638

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 31/176,969/285,921/638, numerators are 31,969,921

Denominators are 176,285,638

The GCF of 31,969,921 is 1 .

LCM of 176,285,638 is 1454640.

The greatest common factor of 31/176,969/285,921/638 = [GCF of 31,969,921]/[LCM of 176,285,638]= 1/1454640

Therefore, the GCF of 31/176,969/285,921/638 is 1/1454640.

Greatest Common Factor of 31,969,921

To find the highest common factor of 31,969,921, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The factors of 921 are 1, 3, 307, 921

The HCF of 31,969,921 is 1.

Lets's calculate GCF of 31,969,921

Greatest Common Factor (GCF) of 31,969,921 By Common Division

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

Greatest Common Factor of 31,969,921 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 969

1,3,17,19,51,57,323,969

Now, list down the factors of 921

1,3,307,921

Greatest Common Factor

We found the factors 31,969,921 . The biggest common factor number is the GCF number.
So the greatest common factor 31,969,921 is 1.

Lets's calculate LCM of 176,285,638

Lowest Common Multiple of 176,285,638 using Common Division

2	176, 285, 638
11	88, 285, 319
	8, 285, 29

∴ So the LCM of the given numbers is 2 x 11 x 8 x 285 x 29 = 1454640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1454640

Therefore, the GCF of Fractions 31/176,969/285,921/638 is 1/1454640

Least Common Multiple of 176,285,638 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 176,285,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(176,285,638) = 1

common factors(in case of two or more numbers have common factors) = 22

GCF(176,285,638) x common factors =1 x 22 = 22

LCM(176,285,638) = ( 176 × 285 × 638 ) / 22

LCM(176,285,638) = 32002080 / 22

LCM(176,285,638) = 1454640

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 31/176, 969/285, 921/638

1. What is the HCF of 31,969,921?

The HCF of 31,969,921 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 31/176, 969/285, 921/638?

Answer: GCF of Numerators as per given numbers 31/176, 969/285, 921/638 is

GCF of Numerators i.e. for 31,969,921 is 1

LCM of denominators i.e. for 176,285,638 is 1454640.

Thus, GCF of Fractions is 1/1454640.Finally, GCF of Fractions for 31/176, 969/285, 921/638 is 1/1454640.