How to Find GCF of 784/374, 704/784?

GCF of 784/374, 704/784

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 784/374, 704/784 i.e 16/146608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/374, 704/784.

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 784/374,704/784?

Given fractions are 784/374,704/784

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 784/374,704/784, numerators are 784,704

Denominators are 374,784

The GCF of 784,704 is 16 .

LCM of 374,784 is 146608.

The greatest common factor of 784/374,704/784 = [GCF of 784,704]/[LCM of 374,784]= 16/146608

Therefore, the GCF of 784/374,704/784 is 16/146608.

Greatest Common Factor of 784,704

To find the highest common factor of 784,704, we have to find the factors of both numbers and list the highest common factor.

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704

The HCF of 784,704 is 16.

Lets's calculate GCF of 784,704

Greatest Common Factor (GCF) of 784,704 By Common Division

2	784, 704
2	392, 352
2	196, 176
2	98, 88
	49, 44

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

Greatest Common Factor of 784,704 By Matching Biggest Common Factor Method

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Now, list down the factors of 704

1,2,4,8,11,16,22,32,44,64,88,176,352,704

Greatest Common Factor

We found the factors 784,704 . The biggest common factor number is the GCF number.
So the greatest common factor 784,704 is 16.

Lets's calculate LCM of 374,784

Lowest Common Multiple of 374,784 using Common Division

2	374, 784
	187, 392

∴ So the LCM of the given numbers is 2 x 187 x 392 = 146608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/146608

Therefore, the GCF of Fractions 784/374,704/784 is 16/146608

Least Common Multiple of 374,784 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 374,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(374,784) = 2

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

GCF(374,784) x common factors =2 x 1 = 2

LCM(374,784) = ( 374 × 784 ) / 2

LCM(374,784) = 293216 / 2

LCM(374,784) = 146608

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FAQs on GCF of Fractions of 784/374, 704/784

1. What is the HCF of 784,704?

The HCF of 784,704 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 784/374, 704/784?

Answer: GCF of Numerators as per given numbers 784/374, 704/784 is

GCF of Numerators i.e. for 784,704 is 16

LCM of denominators i.e. for 374,784 is 146608.

Thus, GCF of Fractions is 16/146608.Finally, GCF of Fractions for 784/374, 704/784 is 16/146608.