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GCF of 165/284, 1267/7904

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 165/284, 1267/7904 i.e 1/561184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/284, 1267/7904.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 165/284,1267/7904?

Given fractions are 165/284,1267/7904

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 165/284,1267/7904, numerators are 165,1267

Denominators are 284,7904

The GCF of 165,1267 is 1 .

LCM of 284,7904 is 561184.

The greatest common factor of 165/284,1267/7904 = [GCF of 165,1267]/[LCM of 284,7904]= 1/561184

Therefore, the GCF of 165/284,1267/7904 is 1/561184.

Greatest Common Factor of 165,1267

To find the highest common factor of 165,1267, we have to find the factors of both numbers and list the highest common factor.

The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165

The factors of 1267 are 1, 7, 181, 1267

The HCF of 165,1267 is 1.

Lets's calculate GCF of 165,1267

Greatest Common Factor (GCF) of 165,1267 By Common Division

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

Greatest Common Factor of 165,1267 By Matching Biggest Common Factor Method

Greatest Common Factor of 165,1267 By Matching Biggest Common Factor Method

Now, list down the factors of 165

:

1,3,5,11,15,33,55,165

Now, list down the factors of 1267

:

1,7,181,1267

Greatest Common Factor

We found the factors 165,1267 . The biggest common factor number is the GCF number.
So the greatest common factor 165,1267 is 1.

Lets's calculate LCM of 284,7904

Lowest Common Multiple of 284,7904 using Common Division

2 284, 7904
2 142, 3952
71, 1976

∴ So the LCM of the given numbers is 2 x 2 x 71 x 1976 = 561184

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/561184

Therefore, the GCF of Fractions 165/284,1267/7904 is 1/561184

Least Common Multiple of 284,7904 with GCF Formula

Least Common Multiple of 284,7904 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 284,7904 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,7904) = 4

common factors(in case of two or more numbers have common factors) = 1

GCF(284,7904) x common factors =4 x 1 = 4

LCM(284,7904) = ( 284 × 7904 ) / 4

LCM(284,7904) = 2244736 / 4

LCM(284,7904) = 561184


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 165/284, 1267/7904

1. What is the HCF of 165,1267?

The HCF of 165,1267 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 165/284, 1267/7904?

Answer: GCF of Numerators as per given numbers 165/284, 1267/7904 is

GCF of Numerators i.e. for 165,1267 is 1

LCM of denominators i.e. for 284,7904 is 561184.

Thus, GCF of Fractions is 1/561184.Finally, GCF of Fractions for 165/284, 1267/7904 is 1/561184.