How to Find GCF of 504/216, 656/458?

GCF of 504/216, 656/458

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 504/216, 656/458 i.e 8/49464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/216, 656/458.

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 504/216,656/458?

Given fractions are 504/216,656/458

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 504/216,656/458, numerators are 504,656

Denominators are 216,458

The GCF of 504,656 is 8 .

LCM of 216,458 is 49464.

The greatest common factor of 504/216,656/458 = [GCF of 504,656]/[LCM of 216,458]= 8/49464

Therefore, the GCF of 504/216,656/458 is 8/49464.

Greatest Common Factor of 504,656

To find the highest common factor of 504,656, we have to find the factors of both numbers and list the highest common factor.

The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504

The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656

The HCF of 504,656 is 8.

Lets's calculate GCF of 504,656

Greatest Common Factor (GCF) of 504,656 By Common Division

2	504, 656
2	252, 328
2	126, 164
	63, 82

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

Greatest Common Factor of 504,656 By Matching Biggest Common Factor Method

Now, list down the factors of 504

1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504

Now, list down the factors of 656

1,2,4,8,16,41,82,164,328,656

Greatest Common Factor

We found the factors 504,656 . The biggest common factor number is the GCF number.
So the greatest common factor 504,656 is 8.

Lets's calculate LCM of 216,458

Lowest Common Multiple of 216,458 using Common Division

2	216, 458
	108, 229

∴ So the LCM of the given numbers is 2 x 108 x 229 = 49464

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/49464

Therefore, the GCF of Fractions 504/216,656/458 is 8/49464

Least Common Multiple of 216,458 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 216,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(216,458) = 2

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

GCF(216,458) x common factors =2 x 1 = 2

LCM(216,458) = ( 216 × 458 ) / 2

LCM(216,458) = 98928 / 2

LCM(216,458) = 49464

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FAQs on GCF of Fractions of 504/216, 656/458

1. What is the HCF of 504,656?

The HCF of 504,656 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 504/216, 656/458?

Answer: GCF of Numerators as per given numbers 504/216, 656/458 is

GCF of Numerators i.e. for 504,656 is 8

LCM of denominators i.e. for 216,458 is 49464.

Thus, GCF of Fractions is 8/49464.Finally, GCF of Fractions for 504/216, 656/458 is 8/49464.