How to Find GCF of 384/109, 910/974?

GCF of 384/109, 910/974

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 384/109, 910/974 i.e 2/106166 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/109, 910/974.

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 384/109,910/974?

Given fractions are 384/109,910/974

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 384/109,910/974, numerators are 384,910

Denominators are 109,974

The GCF of 384,910 is 2 .

LCM of 109,974 is 106166.

The greatest common factor of 384/109,910/974 = [GCF of 384,910]/[LCM of 109,974]= 2/106166

Therefore, the GCF of 384/109,910/974 is 2/106166.

Greatest Common Factor of 384,910

To find the highest common factor of 384,910, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 910 are 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910

The HCF of 384,910 is 2.

Lets's calculate GCF of 384,910

Greatest Common Factor (GCF) of 384,910 By Common Division

2	384, 910
	192, 455

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

Greatest Common Factor of 384,910 By Matching Biggest Common Factor Method

Now, list down the factors of 384

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

Now, list down the factors of 910

1,2,5,7,10,13,14,26,35,65,70,91,130,182,455,910

Greatest Common Factor

We found the factors 384,910 . The biggest common factor number is the GCF number.
So the greatest common factor 384,910 is 2.

Lets's calculate LCM of 109,974

Lowest Common Multiple of 109,974 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 106166

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/106166

Therefore, the GCF of Fractions 384/109,910/974 is 2/106166

Least Common Multiple of 109,974 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 109,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(109,974) = 1

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

GCF(109,974) x common factors =1 x 1 = 1

LCM(109,974) = ( 109 × 974 ) / 1

LCM(109,974) = 106166 / 1

LCM(109,974) = 106166

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FAQs on GCF of Fractions of 384/109, 910/974

1. What is the HCF of 384,910?

The HCF of 384,910 is 2

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 384/109, 910/974?

Answer: GCF of Numerators as per given numbers 384/109, 910/974 is

GCF of Numerators i.e. for 384,910 is 2

LCM of denominators i.e. for 109,974 is 106166.

Thus, GCF of Fractions is 2/106166.Finally, GCF of Fractions for 384/109, 910/974 is 2/106166.