How to Find GCF of 488/20, 816/709?

GCF of 488/20, 816/709

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 488/20, 816/709 i.e 8/14180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 488/20, 816/709.

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 488/20,816/709?

Given fractions are 488/20,816/709

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 488/20,816/709, numerators are 488,816

Denominators are 20,709

The GCF of 488,816 is 8 .

LCM of 20,709 is 14180.

The greatest common factor of 488/20,816/709 = [GCF of 488,816]/[LCM of 20,709]= 8/14180

Therefore, the GCF of 488/20,816/709 is 8/14180.

Greatest Common Factor of 488,816

To find the highest common factor of 488,816, we have to find the factors of both numbers and list the highest common factor.

The factors of 488 are 1, 2, 4, 8, 61, 122, 244, 488

The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816

The HCF of 488,816 is 8.

Lets's calculate GCF of 488,816

Greatest Common Factor (GCF) of 488,816 By Common Division

2	488, 816
2	244, 408
2	122, 204
	61, 102

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 488,816 By Matching Biggest Common Factor Method

Now, list down the factors of 488

1,2,4,8,61,122,244,488

Now, list down the factors of 816

1,2,3,4,6,8,12,16,17,24,34,48,51,68,102,136,204,272,408,816

Greatest Common Factor

We found the factors 488,816 . The biggest common factor number is the GCF number.
So the greatest common factor 488,816 is 8.

Lets's calculate LCM of 20,709

Lowest Common Multiple of 20,709 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 14180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/14180

Therefore, the GCF of Fractions 488/20,816/709 is 8/14180

Least Common Multiple of 20,709 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 20,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,709) = 1

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

GCF(20,709) x common factors =1 x 1 = 1

LCM(20,709) = ( 20 × 709 ) / 1

LCM(20,709) = 14180 / 1

LCM(20,709) = 14180

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FAQs on GCF of Fractions of 488/20, 816/709

1. What is the HCF of 488,816?

The HCF of 488,816 is 8

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 488/20, 816/709?

Answer: GCF of Numerators as per given numbers 488/20, 816/709 is

GCF of Numerators i.e. for 488,816 is 8

LCM of denominators i.e. for 20,709 is 14180.

Thus, GCF of Fractions is 8/14180.Finally, GCF of Fractions for 488/20, 816/709 is 8/14180.