How to Find GCF of 992/863, 6560/514?

GCF of 992/863, 6560/514

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 992/863, 6560/514 i.e 32/443582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/863, 6560/514.

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 992/863,6560/514?

Given fractions are 992/863,6560/514

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 992/863,6560/514, numerators are 992,6560

Denominators are 863,514

The GCF of 992,6560 is 32 .

LCM of 863,514 is 443582.

The greatest common factor of 992/863,6560/514 = [GCF of 992,6560]/[LCM of 863,514]= 32/443582

Therefore, the GCF of 992/863,6560/514 is 32/443582.

Greatest Common Factor of 992,6560

To find the highest common factor of 992,6560, we have to find the factors of both numbers and list the highest common factor.

The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

The factors of 6560 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 41, 80, 82, 160, 164, 205, 328, 410, 656, 820, 1312, 1640, 3280, 6560

The HCF of 992,6560 is 32.

Lets's calculate GCF of 992,6560

Greatest Common Factor (GCF) of 992,6560 By Common Division

2	992, 6560
2	496, 3280
2	248, 1640
2	124, 820
2	62, 410
	31, 205

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 992,6560 By Matching Biggest Common Factor Method

Now, list down the factors of 992

1,2,4,8,16,31,32,62,124,248,496,992

Now, list down the factors of 6560

1,2,4,5,8,10,16,20,32,40,41,80,82,160,164,205,328,410,656,820,1312,1640,3280,6560

Greatest Common Factor

We found the factors 992,6560 . The biggest common factor number is the GCF number.
So the greatest common factor 992,6560 is 32.

Lets's calculate LCM of 863,514

Lowest Common Multiple of 863,514 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 443582

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/443582

Therefore, the GCF of Fractions 992/863,6560/514 is 32/443582

Least Common Multiple of 863,514 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 863,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(863,514) = 1

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

GCF(863,514) x common factors =1 x 1 = 1

LCM(863,514) = ( 863 × 514 ) / 1

LCM(863,514) = 443582 / 1

LCM(863,514) = 443582

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FAQs on GCF of Fractions of 992/863, 6560/514

1. What is the HCF of 992,6560?

The HCF of 992,6560 is 32

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 992/863, 6560/514?

Answer: GCF of Numerators as per given numbers 992/863, 6560/514 is

GCF of Numerators i.e. for 992,6560 is 32

LCM of denominators i.e. for 863,514 is 443582.

Thus, GCF of Fractions is 32/443582.Finally, GCF of Fractions for 992/863, 6560/514 is 32/443582.