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GCF of 663/20, 299/714

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 663/20, 299/714 i.e 13/7140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 663/20, 299/714.

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 663/20,299/714?

Given fractions are 663/20,299/714

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 663/20,299/714, numerators are 663,299

Denominators are 20,714

The GCF of 663,299 is 13 .

LCM of 20,714 is 7140.

The greatest common factor of 663/20,299/714 = [GCF of 663,299]/[LCM of 20,714]= 13/7140

Therefore, the GCF of 663/20,299/714 is 13/7140.

Greatest Common Factor of 663,299

To find the highest common factor of 663,299, we have to find the factors of both numbers and list the highest common factor.

The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663

The factors of 299 are 1, 13, 23, 299

The HCF of 663,299 is 13.

Lets's calculate GCF of 663,299

Greatest Common Factor (GCF) of 663,299 By Common Division

13 663, 299
51, 23

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 663,299 By Matching Biggest Common Factor Method

Greatest Common Factor of 663,299 By Matching Biggest Common Factor Method

Now, list down the factors of 663

:

1,3,13,17,39,51,221,663

Now, list down the factors of 299

:

1,13,23,299

Greatest Common Factor

We found the factors 663,299 . The biggest common factor number is the GCF number.
So the greatest common factor 663,299 is 13.

Lets's calculate LCM of 20,714

Lowest Common Multiple of 20,714 using Common Division

2 20, 714
10, 357

∴ So the LCM of the given numbers is 2 x 10 x 357 = 7140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/7140

Therefore, the GCF of Fractions 663/20,299/714 is 13/7140

Least Common Multiple of 20,714 with GCF Formula

Least Common Multiple of 20,714 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 20,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,714) = 2

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

GCF(20,714) x common factors =2 x 1 = 2

LCM(20,714) = ( 20 × 714 ) / 2

LCM(20,714) = 14280 / 2

LCM(20,714) = 7140


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FAQs on GCF of Fractions of 663/20, 299/714

1. What is the HCF of 663,299?

The HCF of 663,299 is 13

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 663/20, 299/714?

Answer: GCF of Numerators as per given numbers 663/20, 299/714 is

GCF of Numerators i.e. for 663,299 is 13

LCM of denominators i.e. for 20,714 is 7140.

Thus, GCF of Fractions is 13/7140.Finally, GCF of Fractions for 663/20, 299/714 is 13/7140.