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GCF of 642/289, 384/802

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 642/289, 384/802 i.e 6/231778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/289, 384/802.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 642/289,384/802?

Given fractions are 642/289,384/802

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 642/289,384/802, numerators are 642,384

Denominators are 289,802

The GCF of 642,384 is 6 .

LCM of 289,802 is 231778.

The greatest common factor of 642/289,384/802 = [GCF of 642,384]/[LCM of 289,802]= 6/231778

Therefore, the GCF of 642/289,384/802 is 6/231778.

Greatest Common Factor of 642,384

To find the highest common factor of 642,384, we have to find the factors of both numbers and list the highest common factor.

The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642

The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

The HCF of 642,384 is 6.

Lets's calculate GCF of 642,384

Greatest Common Factor (GCF) of 642,384 By Common Division

2 642, 384
3 321, 192
107, 64

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 642,384 By Matching Biggest Common Factor Method

Greatest Common Factor of 642,384 By Matching Biggest Common Factor Method

Now, list down the factors of 642

:

1,2,3,6,107,214,321,642

Now, list down the factors of 384

:

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

Greatest Common Factor

We found the factors 642,384 . The biggest common factor number is the GCF number.
So the greatest common factor 642,384 is 6.

Lets's calculate LCM of 289,802

Lowest Common Multiple of 289,802 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 231778

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/231778

Therefore, the GCF of Fractions 642/289,384/802 is 6/231778

Least Common Multiple of 289,802 with GCF Formula

Least Common Multiple of 289,802 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 289,802 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,802) = 1

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

GCF(289,802) x common factors =1 x 1 = 1

LCM(289,802) = ( 289 × 802 ) / 1

LCM(289,802) = 231778 / 1

LCM(289,802) = 231778


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FAQs on GCF of Fractions of 642/289, 384/802

1. What is the HCF of 642,384?

The HCF of 642,384 is 6

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 642/289, 384/802?

Answer: GCF of Numerators as per given numbers 642/289, 384/802 is

GCF of Numerators i.e. for 642,384 is 6

LCM of denominators i.e. for 289,802 is 231778.

Thus, GCF of Fractions is 6/231778.Finally, GCF of Fractions for 642/289, 384/802 is 6/231778.