How to Find GCF of 6614/208, 8576/8604?

GCF of 6614/208, 8576/8604

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 6614/208, 8576/8604 i.e 2/447408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6614/208, 8576/8604.

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 6614/208,8576/8604?

Given fractions are 6614/208,8576/8604

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 6614/208,8576/8604, numerators are 6614,8576

Denominators are 208,8604

The GCF of 6614,8576 is 2 .

LCM of 208,8604 is 447408.

The greatest common factor of 6614/208,8576/8604 = [GCF of 6614,8576]/[LCM of 208,8604]= 2/447408

Therefore, the GCF of 6614/208,8576/8604 is 2/447408.

Greatest Common Factor of 6614,8576

To find the highest common factor of 6614,8576, we have to find the factors of both numbers and list the highest common factor.

The factors of 6614 are 1, 2, 3307, 6614

The factors of 8576 are 1, 2, 4, 8, 16, 32, 64, 67, 128, 134, 268, 536, 1072, 2144, 4288, 8576

The HCF of 6614,8576 is 2.

Lets's calculate GCF of 6614,8576

Greatest Common Factor (GCF) of 6614,8576 By Common Division

2	6614, 8576
	3307, 4288

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

Greatest Common Factor of 6614,8576 By Matching Biggest Common Factor Method

Now, list down the factors of 6614

1,2,3307,6614

Now, list down the factors of 8576

1,2,4,8,16,32,64,67,128,134,268,536,1072,2144,4288,8576

Greatest Common Factor

We found the factors 6614,8576 . The biggest common factor number is the GCF number.
So the greatest common factor 6614,8576 is 2.

Lets's calculate LCM of 208,8604

Lowest Common Multiple of 208,8604 using Common Division

2	208, 8604
2	104, 4302
	52, 2151

∴ So the LCM of the given numbers is 2 x 2 x 52 x 2151 = 447408

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/447408

Therefore, the GCF of Fractions 6614/208,8576/8604 is 2/447408

Least Common Multiple of 208,8604 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 208,8604 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,8604) = 4

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

GCF(208,8604) x common factors =4 x 1 = 4

LCM(208,8604) = ( 208 × 8604 ) / 4

LCM(208,8604) = 1789632 / 4

LCM(208,8604) = 447408

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FAQs on GCF of Fractions of 6614/208, 8576/8604

1. What is the HCF of 6614,8576?

The HCF of 6614,8576 is 2

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 6614/208, 8576/8604?

Answer: GCF of Numerators as per given numbers 6614/208, 8576/8604 is

GCF of Numerators i.e. for 6614,8576 is 2

LCM of denominators i.e. for 208,8604 is 447408.

Thus, GCF of Fractions is 2/447408.Finally, GCF of Fractions for 6614/208, 8576/8604 is 2/447408.