How to Find GCF of 83/256, 5709/8184?

GCF of 83/256, 5709/8184

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 83/256, 5709/8184 i.e 1/261888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 83/256, 5709/8184.

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 83/256,5709/8184?

Given fractions are 83/256,5709/8184

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 83/256,5709/8184, numerators are 83,5709

Denominators are 256,8184

The GCF of 83,5709 is 1 .

LCM of 256,8184 is 261888.

The greatest common factor of 83/256,5709/8184 = [GCF of 83,5709]/[LCM of 256,8184]= 1/261888

Therefore, the GCF of 83/256,5709/8184 is 1/261888.

Greatest Common Factor of 83,5709

To find the highest common factor of 83,5709, we have to find the factors of both numbers and list the highest common factor.

The factors of 83 are 1, 83

The factors of 5709 are 1, 3, 11, 33, 173, 519, 1903, 5709

The HCF of 83,5709 is 1.

Lets's calculate GCF of 83,5709

Greatest Common Factor (GCF) of 83,5709 By Common Division

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

Greatest Common Factor of 83,5709 By Matching Biggest Common Factor Method

Now, list down the factors of 83

1,83

Now, list down the factors of 5709

1,3,11,33,173,519,1903,5709

Greatest Common Factor

We found the factors 83,5709 . The biggest common factor number is the GCF number.
So the greatest common factor 83,5709 is 1.

Lets's calculate LCM of 256,8184

Lowest Common Multiple of 256,8184 using Common Division

2	256, 8184
2	128, 4092
2	64, 2046
	32, 1023

∴ So the LCM of the given numbers is 2 x 2 x 2 x 32 x 1023 = 261888

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/261888

Therefore, the GCF of Fractions 83/256,5709/8184 is 1/261888

Least Common Multiple of 256,8184 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 256,8184 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(256,8184) = 8

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

GCF(256,8184) x common factors =8 x 1 = 8

LCM(256,8184) = ( 256 × 8184 ) / 8

LCM(256,8184) = 2095104 / 8

LCM(256,8184) = 261888

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FAQs on GCF of Fractions of 83/256, 5709/8184

1. What is the HCF of 83,5709?

The HCF of 83,5709 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 83/256, 5709/8184?

Answer: GCF of Numerators as per given numbers 83/256, 5709/8184 is

GCF of Numerators i.e. for 83,5709 is 1

LCM of denominators i.e. for 256,8184 is 261888.

Thus, GCF of Fractions is 1/261888.Finally, GCF of Fractions for 83/256, 5709/8184 is 1/261888.