How to Find GCF of 8509/268, 4324/2204?

GCF of 8509/268, 4324/2204

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 8509/268, 4324/2204 i.e 1/147668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8509/268, 4324/2204.

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 8509/268,4324/2204?

Given fractions are 8509/268,4324/2204

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 8509/268,4324/2204, numerators are 8509,4324

Denominators are 268,2204

The GCF of 8509,4324 is 1 .

LCM of 268,2204 is 147668.

The greatest common factor of 8509/268,4324/2204 = [GCF of 8509,4324]/[LCM of 268,2204]= 1/147668

Therefore, the GCF of 8509/268,4324/2204 is 1/147668.

Greatest Common Factor of 8509,4324

To find the highest common factor of 8509,4324, we have to find the factors of both numbers and list the highest common factor.

The factors of 8509 are 1, 67, 127, 8509

The factors of 4324 are 1, 2, 4, 23, 46, 47, 92, 94, 188, 1081, 2162, 4324

The HCF of 8509,4324 is 1.

Lets's calculate GCF of 8509,4324

Greatest Common Factor (GCF) of 8509,4324 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 8509,4324 By Matching Biggest Common Factor Method

Now, list down the factors of 8509

1,67,127,8509

Now, list down the factors of 4324

1,2,4,23,46,47,92,94,188,1081,2162,4324

Greatest Common Factor

We found the factors 8509,4324 . The biggest common factor number is the GCF number.
So the greatest common factor 8509,4324 is 1.

Lets's calculate LCM of 268,2204

Lowest Common Multiple of 268,2204 using Common Division

2	268, 2204
2	134, 1102
	67, 551

∴ So the LCM of the given numbers is 2 x 2 x 67 x 551 = 147668

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/147668

Therefore, the GCF of Fractions 8509/268,4324/2204 is 1/147668

Least Common Multiple of 268,2204 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 268,2204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,2204) = 4

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

GCF(268,2204) x common factors =4 x 1 = 4

LCM(268,2204) = ( 268 × 2204 ) / 4

LCM(268,2204) = 590672 / 4

LCM(268,2204) = 147668

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FAQs on GCF of Fractions of 8509/268, 4324/2204

1. What is the HCF of 8509,4324?

The HCF of 8509,4324 is 1

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 8509/268, 4324/2204?

Answer: GCF of Numerators as per given numbers 8509/268, 4324/2204 is

GCF of Numerators i.e. for 8509,4324 is 1

LCM of denominators i.e. for 268,2204 is 147668.

Thus, GCF of Fractions is 1/147668.Finally, GCF of Fractions for 8509/268, 4324/2204 is 1/147668.