How to Find GCF of 768/314, 544/200?

GCF of 768/314, 544/200

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 768/314, 544/200 i.e 32/31400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/314, 544/200.

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 768/314,544/200?

Given fractions are 768/314,544/200

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 768/314,544/200, numerators are 768,544

Denominators are 314,200

The GCF of 768,544 is 32 .

LCM of 314,200 is 31400.

The greatest common factor of 768/314,544/200 = [GCF of 768,544]/[LCM of 314,200]= 32/31400

Therefore, the GCF of 768/314,544/200 is 32/31400.

Greatest Common Factor of 768,544

To find the highest common factor of 768,544, we have to find the factors of both numbers and list the highest common factor.

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544

The HCF of 768,544 is 32.

Lets's calculate GCF of 768,544

Greatest Common Factor (GCF) of 768,544 By Common Division

2	768, 544
2	384, 272
2	192, 136
2	96, 68
2	48, 34
	24, 17

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

Greatest Common Factor of 768,544 By Matching Biggest Common Factor Method

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Now, list down the factors of 544

1,2,4,8,16,17,32,34,68,136,272,544

Greatest Common Factor

We found the factors 768,544 . The biggest common factor number is the GCF number.
So the greatest common factor 768,544 is 32.

Lets's calculate LCM of 314,200

Lowest Common Multiple of 314,200 using Common Division

2	314, 200
	157, 100

∴ So the LCM of the given numbers is 2 x 157 x 100 = 31400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/31400

Therefore, the GCF of Fractions 768/314,544/200 is 32/31400

Least Common Multiple of 314,200 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 314,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,200) = 2

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

GCF(314,200) x common factors =2 x 1 = 2

LCM(314,200) = ( 314 × 200 ) / 2

LCM(314,200) = 62800 / 2

LCM(314,200) = 31400

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FAQs on GCF of Fractions of 768/314, 544/200

1. What is the HCF of 768,544?

The HCF of 768,544 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 768/314, 544/200?

Answer: GCF of Numerators as per given numbers 768/314, 544/200 is

GCF of Numerators i.e. for 768,544 is 32

LCM of denominators i.e. for 314,200 is 31400.

Thus, GCF of Fractions is 32/31400.Finally, GCF of Fractions for 768/314, 544/200 is 32/31400.