How to Find GCF of 208/21, 640/565?

GCF of 208/21, 640/565

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 208/21, 640/565 i.e 16/11865 easily. The following is the detailed procedure to determine the greatest common factor of fractions 208/21, 640/565.

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 208/21,640/565?

Given fractions are 208/21,640/565

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 208/21,640/565, numerators are 208,640

Denominators are 21,565

The GCF of 208,640 is 16 .

LCM of 21,565 is 11865.

The greatest common factor of 208/21,640/565 = [GCF of 208,640]/[LCM of 21,565]= 16/11865

Therefore, the GCF of 208/21,640/565 is 16/11865.

Greatest Common Factor of 208,640

To find the highest common factor of 208,640, we have to find the factors of both numbers and list the highest common factor.

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640

The HCF of 208,640 is 16.

Lets's calculate GCF of 208,640

Greatest Common Factor (GCF) of 208,640 By Common Division

2	208, 640
2	104, 320
2	52, 160
2	26, 80
	13, 40

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 208,640 By Matching Biggest Common Factor Method

Now, list down the factors of 208

1,2,4,8,13,16,26,52,104,208

Now, list down the factors of 640

1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640

Greatest Common Factor

We found the factors 208,640 . The biggest common factor number is the GCF number.
So the greatest common factor 208,640 is 16.

Lets's calculate LCM of 21,565

Lowest Common Multiple of 21,565 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11865

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/11865

Therefore, the GCF of Fractions 208/21,640/565 is 16/11865

Least Common Multiple of 21,565 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 21,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,565) = 1

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

GCF(21,565) x common factors =1 x 1 = 1

LCM(21,565) = ( 21 × 565 ) / 1

LCM(21,565) = 11865 / 1

LCM(21,565) = 11865

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FAQs on GCF of Fractions of 208/21, 640/565

1. What is the HCF of 208,640?

The HCF of 208,640 is 16

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 208/21, 640/565?

Answer: GCF of Numerators as per given numbers 208/21, 640/565 is

GCF of Numerators i.e. for 208,640 is 16

LCM of denominators i.e. for 21,565 is 11865.

Thus, GCF of Fractions is 16/11865.Finally, GCF of Fractions for 208/21, 640/565 is 16/11865.