How to Find GCF of 488/217, 512/627?

GCF of 488/217, 512/627

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 488/217, 512/627 i.e 8/136059 easily. The following is the detailed procedure to determine the greatest common factor of fractions 488/217, 512/627.

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 488/217,512/627?

Given fractions are 488/217,512/627

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 488/217,512/627, numerators are 488,512

Denominators are 217,627

The GCF of 488,512 is 8 .

LCM of 217,627 is 136059.

The greatest common factor of 488/217,512/627 = [GCF of 488,512]/[LCM of 217,627]= 8/136059

Therefore, the GCF of 488/217,512/627 is 8/136059.

Greatest Common Factor of 488,512

To find the highest common factor of 488,512, 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 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 488,512 is 8.

Lets's calculate GCF of 488,512

Greatest Common Factor (GCF) of 488,512 By Common Division

2	488, 512
2	244, 256
2	122, 128
	61, 64

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

Greatest Common Factor of 488,512 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 512

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

Greatest Common Factor

We found the factors 488,512 . The biggest common factor number is the GCF number.
So the greatest common factor 488,512 is 8.

Lets's calculate LCM of 217,627

Lowest Common Multiple of 217,627 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 136059

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/136059

Therefore, the GCF of Fractions 488/217,512/627 is 8/136059

Least Common Multiple of 217,627 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 217,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(217,627) = 1

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

GCF(217,627) x common factors =1 x 1 = 1

LCM(217,627) = ( 217 × 627 ) / 1

LCM(217,627) = 136059 / 1

LCM(217,627) = 136059

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FAQs on GCF of Fractions of 488/217, 512/627

1. What is the HCF of 488,512?

The HCF of 488,512 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 488/217, 512/627?

Answer: GCF of Numerators as per given numbers 488/217, 512/627 is

GCF of Numerators i.e. for 488,512 is 8

LCM of denominators i.e. for 217,627 is 136059.

Thus, GCF of Fractions is 8/136059.Finally, GCF of Fractions for 488/217, 512/627 is 8/136059.