How to Find GCF of 896/51, 208/608?

GCF of 896/51, 208/608

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 896/51, 208/608 i.e 16/31008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 896/51, 208/608.

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 896/51,208/608?

Given fractions are 896/51,208/608

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 896/51,208/608, numerators are 896,208

Denominators are 51,608

The GCF of 896,208 is 16 .

LCM of 51,608 is 31008.

The greatest common factor of 896/51,208/608 = [GCF of 896,208]/[LCM of 51,608]= 16/31008

Therefore, the GCF of 896/51,208/608 is 16/31008.

Greatest Common Factor of 896,208

To find the highest common factor of 896,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896

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

The HCF of 896,208 is 16.

Lets's calculate GCF of 896,208

Greatest Common Factor (GCF) of 896,208 By Common Division

2	896, 208
2	448, 104
2	224, 52
2	112, 26
	56, 13

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

Greatest Common Factor of 896,208 By Matching Biggest Common Factor Method

Now, list down the factors of 896

1,2,4,7,8,14,16,28,32,56,64,112,128,224,448,896

Now, list down the factors of 208

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

Greatest Common Factor

We found the factors 896,208 . The biggest common factor number is the GCF number.
So the greatest common factor 896,208 is 16.

Lets's calculate LCM of 51,608

Lowest Common Multiple of 51,608 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 31008

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/31008

Therefore, the GCF of Fractions 896/51,208/608 is 16/31008

Least Common Multiple of 51,608 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 51,608 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,608) = 1

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

GCF(51,608) x common factors =1 x 1 = 1

LCM(51,608) = ( 51 × 608 ) / 1

LCM(51,608) = 31008 / 1

LCM(51,608) = 31008

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FAQs on GCF of Fractions of 896/51, 208/608

1. What is the HCF of 896,208?

The HCF of 896,208 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 896/51, 208/608?

Answer: GCF of Numerators as per given numbers 896/51, 208/608 is

GCF of Numerators i.e. for 896,208 is 16

LCM of denominators i.e. for 51,608 is 31008.

Thus, GCF of Fractions is 16/31008.Finally, GCF of Fractions for 896/51, 208/608 is 16/31008.