How to Find GCF of 11/686, 54/312, 564/128?

GCF of 11/686, 54/312, 564/128

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 11/686, 54/312, 564/128 i.e 1/1712256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 11/686, 54/312, 564/128.

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 11/686,54/312,564/128?

Given fractions are 11/686,54/312,564/128

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 11/686,54/312,564/128, numerators are 11,54,564

Denominators are 686,312,128

The GCF of 11,54,564 is 1 .

LCM of 686,312,128 is 1712256.

The greatest common factor of 11/686,54/312,564/128 = [GCF of 11,54,564]/[LCM of 686,312,128]= 1/1712256

Therefore, the GCF of 11/686,54/312,564/128 is 1/1712256.

Greatest Common Factor of 11,54,564

To find the highest common factor of 11,54,564, we have to find the factors of both numbers and list the highest common factor.

The factors of 11 are 1, 11

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

The HCF of 11,54,564 is 1.

Lets's calculate GCF of 11,54,564

Greatest Common Factor (GCF) of 11,54,564 By Common Division

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

Greatest Common Factor of 11,54,564 By Matching Biggest Common Factor Method

Now, list down the factors of 11

1,11

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 564

1,2,3,4,6,12,47,94,141,188,282,564

Greatest Common Factor

We found the factors 11,54,564 . The biggest common factor number is the GCF number.
So the greatest common factor 11,54,564 is 1.

Lets's calculate LCM of 686,312,128

Lowest Common Multiple of 686,312,128 using Common Division

2	686, 312, 128
2	343, 156, 64
2	343, 78, 32
	343, 39, 16

∴ So the LCM of the given numbers is 2 x 2 x 2 x 343 x 39 x 16 = 1712256

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1712256

Therefore, the GCF of Fractions 11/686,54/312,564/128 is 1/1712256

Least Common Multiple of 686,312,128 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 686,312,128 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(686,312,128) = 2

common factors(in case of two or more numbers have common factors) = 8

GCF(686,312,128) x common factors =2 x 8 = 16

LCM(686,312,128) = ( 686 × 312 × 128 ) / 16

LCM(686,312,128) = 27396096 / 16

LCM(686,312,128) = 1712256

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FAQs on GCF of Fractions of 11/686, 54/312, 564/128

1. What is the HCF of 11,54,564?

The HCF of 11,54,564 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 11/686, 54/312, 564/128?

Answer: GCF of Numerators as per given numbers 11/686, 54/312, 564/128 is

GCF of Numerators i.e. for 11,54,564 is 1

LCM of denominators i.e. for 686,312,128 is 1712256.

Thus, GCF of Fractions is 1/1712256.Finally, GCF of Fractions for 11/686, 54/312, 564/128 is 1/1712256.