How to Find GCF of 5771/144, 6714/864?

GCF of 5771/144, 6714/864

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 5771/144, 6714/864 i.e 1/864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5771/144, 6714/864.

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 5771/144,6714/864?

Given fractions are 5771/144,6714/864

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 5771/144,6714/864, numerators are 5771,6714

Denominators are 144,864

The GCF of 5771,6714 is 1 .

LCM of 144,864 is 864.

The greatest common factor of 5771/144,6714/864 = [GCF of 5771,6714]/[LCM of 144,864]= 1/864

Therefore, the GCF of 5771/144,6714/864 is 1/864.

Greatest Common Factor of 5771,6714

To find the highest common factor of 5771,6714, we have to find the factors of both numbers and list the highest common factor.

The factors of 5771 are 1, 29, 199, 5771

The factors of 6714 are 1, 2, 3, 6, 9, 18, 373, 746, 1119, 2238, 3357, 6714

The HCF of 5771,6714 is 1.

Lets's calculate GCF of 5771,6714

Greatest Common Factor (GCF) of 5771,6714 By Common Division

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

Greatest Common Factor of 5771,6714 By Matching Biggest Common Factor Method

Now, list down the factors of 5771

1,29,199,5771

Now, list down the factors of 6714

1,2,3,6,9,18,373,746,1119,2238,3357,6714

Greatest Common Factor

We found the factors 5771,6714 . The biggest common factor number is the GCF number.
So the greatest common factor 5771,6714 is 1.

Lets's calculate LCM of 144,864

Lowest Common Multiple of 144,864 using Common Division

2	144, 864
2	72, 432
2	36, 216
2	18, 108
3	9, 54
3	3, 18
	1, 6

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 3 x 1 x 6 = 864

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/864

Therefore, the GCF of Fractions 5771/144,6714/864 is 1/864

Least Common Multiple of 144,864 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 144,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(144,864) = 144

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

GCF(144,864) x common factors =144 x 1 = 144

LCM(144,864) = ( 144 × 864 ) / 144

LCM(144,864) = 124416 / 144

LCM(144,864) = 864

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FAQs on GCF of Fractions of 5771/144, 6714/864

1. What is the HCF of 5771,6714?

The HCF of 5771,6714 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 5771/144, 6714/864?

Answer: GCF of Numerators as per given numbers 5771/144, 6714/864 is

GCF of Numerators i.e. for 5771,6714 is 1

LCM of denominators i.e. for 144,864 is 864.

Thus, GCF of Fractions is 1/864.Finally, GCF of Fractions for 5771/144, 6714/864 is 1/864.