How to Find GCF of 5772/560, 1751/256?

GCF of 5772/560, 1751/256

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 5772/560, 1751/256 i.e 1/8960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5772/560, 1751/256.

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 5772/560,1751/256?

Given fractions are 5772/560,1751/256

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 5772/560,1751/256, numerators are 5772,1751

Denominators are 560,256

The GCF of 5772,1751 is 1 .

LCM of 560,256 is 8960.

The greatest common factor of 5772/560,1751/256 = [GCF of 5772,1751]/[LCM of 560,256]= 1/8960

Therefore, the GCF of 5772/560,1751/256 is 1/8960.

Greatest Common Factor of 5772,1751

To find the highest common factor of 5772,1751, we have to find the factors of both numbers and list the highest common factor.

The factors of 5772 are 1, 2, 3, 4, 6, 12, 13, 26, 37, 39, 52, 74, 78, 111, 148, 156, 222, 444, 481, 962, 1443, 1924, 2886, 5772

The factors of 1751 are 1, 17, 103, 1751

The HCF of 5772,1751 is 1.

Lets's calculate GCF of 5772,1751

Greatest Common Factor (GCF) of 5772,1751 By Common Division

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

Greatest Common Factor of 5772,1751 By Matching Biggest Common Factor Method

Now, list down the factors of 5772

1,2,3,4,6,12,13,26,37,39,52,74,78,111,148,156,222,444,481,962,1443,1924,2886,5772

Now, list down the factors of 1751

1,17,103,1751

Greatest Common Factor

We found the factors 5772,1751 . The biggest common factor number is the GCF number.
So the greatest common factor 5772,1751 is 1.

Lets's calculate LCM of 560,256

Lowest Common Multiple of 560,256 using Common Division

2	560, 256
2	280, 128
2	140, 64
2	70, 32
	35, 16

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 35 x 16 = 8960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8960

Therefore, the GCF of Fractions 5772/560,1751/256 is 1/8960

Least Common Multiple of 560,256 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 560,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(560,256) = 16

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

GCF(560,256) x common factors =16 x 1 = 16

LCM(560,256) = ( 560 × 256 ) / 16

LCM(560,256) = 143360 / 16

LCM(560,256) = 8960

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FAQs on GCF of Fractions of 5772/560, 1751/256

1. What is the HCF of 5772,1751?

The HCF of 5772,1751 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 5772/560, 1751/256?

Answer: GCF of Numerators as per given numbers 5772/560, 1751/256 is

GCF of Numerators i.e. for 5772,1751 is 1

LCM of denominators i.e. for 560,256 is 8960.

Thus, GCF of Fractions is 1/8960.Finally, GCF of Fractions for 5772/560, 1751/256 is 1/8960.