How to Find GCF of 1734/645, 3678/2248?

GCF of 1734/645, 3678/2248

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 1734/645, 3678/2248 i.e 6/1449960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1734/645, 3678/2248.

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 1734/645,3678/2248?

Given fractions are 1734/645,3678/2248

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 1734/645,3678/2248, numerators are 1734,3678

Denominators are 645,2248

The GCF of 1734,3678 is 6 .

LCM of 645,2248 is 1449960.

The greatest common factor of 1734/645,3678/2248 = [GCF of 1734,3678]/[LCM of 645,2248]= 6/1449960

Therefore, the GCF of 1734/645,3678/2248 is 6/1449960.

Greatest Common Factor of 1734,3678

To find the highest common factor of 1734,3678, we have to find the factors of both numbers and list the highest common factor.

The factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734

The factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678

The HCF of 1734,3678 is 6.

Lets's calculate GCF of 1734,3678

Greatest Common Factor (GCF) of 1734,3678 By Common Division

2	1734, 3678
3	867, 1839
	289, 613

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 1734,3678 By Matching Biggest Common Factor Method

Now, list down the factors of 1734

1,2,3,6,17,34,51,102,289,578,867,1734

Now, list down the factors of 3678

1,2,3,6,613,1226,1839,3678

Greatest Common Factor

We found the factors 1734,3678 . The biggest common factor number is the GCF number.
So the greatest common factor 1734,3678 is 6.

Lets's calculate LCM of 645,2248

Lowest Common Multiple of 645,2248 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1449960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1449960

Therefore, the GCF of Fractions 1734/645,3678/2248 is 6/1449960

Least Common Multiple of 645,2248 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 645,2248 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(645,2248) = 1

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

GCF(645,2248) x common factors =1 x 1 = 1

LCM(645,2248) = ( 645 × 2248 ) / 1

LCM(645,2248) = 1449960 / 1

LCM(645,2248) = 1449960

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FAQs on GCF of Fractions of 1734/645, 3678/2248

1. What is the HCF of 1734,3678?

The HCF of 1734,3678 is 6

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 1734/645, 3678/2248?

Answer: GCF of Numerators as per given numbers 1734/645, 3678/2248 is

GCF of Numerators i.e. for 1734,3678 is 6

LCM of denominators i.e. for 645,2248 is 1449960.

Thus, GCF of Fractions is 6/1449960.Finally, GCF of Fractions for 1734/645, 3678/2248 is 6/1449960.