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GCF of 669/14, 512/180

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 669/14, 512/180 i.e 1/1260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 669/14, 512/180.

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 669/14,512/180?

Given fractions are 669/14,512/180

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 669/14,512/180, numerators are 669,512

Denominators are 14,180

The GCF of 669,512 is 1 .

LCM of 14,180 is 1260.

The greatest common factor of 669/14,512/180 = [GCF of 669,512]/[LCM of 14,180]= 1/1260

Therefore, the GCF of 669/14,512/180 is 1/1260.

Greatest Common Factor of 669,512

To find the highest common factor of 669,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 669 are 1, 3, 223, 669

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 669,512 is 1.

Lets's calculate GCF of 669,512

Greatest Common Factor (GCF) of 669,512 By Common Division

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

Greatest Common Factor of 669,512 By Matching Biggest Common Factor Method

Greatest Common Factor of 669,512 By Matching Biggest Common Factor Method

Now, list down the factors of 669

:

1,3,223,669

Now, list down the factors of 512

:

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 669,512 . The biggest common factor number is the GCF number.
So the greatest common factor 669,512 is 1.

Lets's calculate LCM of 14,180

Lowest Common Multiple of 14,180 using Common Division

2 14, 180
7, 90

∴ So the LCM of the given numbers is 2 x 7 x 90 = 1260

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1260

Therefore, the GCF of Fractions 669/14,512/180 is 1/1260

Least Common Multiple of 14,180 with GCF Formula

Least Common Multiple of 14,180 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 14,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,180) = 2

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

GCF(14,180) x common factors =2 x 1 = 2

LCM(14,180) = ( 14 × 180 ) / 2

LCM(14,180) = 2520 / 2

LCM(14,180) = 1260


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FAQs on GCF of Fractions of 669/14, 512/180

1. What is the HCF of 669,512?

The HCF of 669,512 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 669/14, 512/180?

Answer: GCF of Numerators as per given numbers 669/14, 512/180 is

GCF of Numerators i.e. for 669,512 is 1

LCM of denominators i.e. for 14,180 is 1260.

Thus, GCF of Fractions is 1/1260.Finally, GCF of Fractions for 669/14, 512/180 is 1/1260.