How to Find GCF of 1742/200, 3662/6512?

GCF of 1742/200, 3662/6512

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 1742/200, 3662/6512 i.e 2/162800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1742/200, 3662/6512.

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 1742/200,3662/6512?

Given fractions are 1742/200,3662/6512

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 1742/200,3662/6512, numerators are 1742,3662

Denominators are 200,6512

The GCF of 1742,3662 is 2 .

LCM of 200,6512 is 162800.

The greatest common factor of 1742/200,3662/6512 = [GCF of 1742,3662]/[LCM of 200,6512]= 2/162800

Therefore, the GCF of 1742/200,3662/6512 is 2/162800.

Greatest Common Factor of 1742,3662

To find the highest common factor of 1742,3662, we have to find the factors of both numbers and list the highest common factor.

The factors of 1742 are 1, 2, 13, 26, 67, 134, 871, 1742

The factors of 3662 are 1, 2, 1831, 3662

The HCF of 1742,3662 is 2.

Lets's calculate GCF of 1742,3662

Greatest Common Factor (GCF) of 1742,3662 By Common Division

2	1742, 3662
	871, 1831

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

Greatest Common Factor of 1742,3662 By Matching Biggest Common Factor Method

Now, list down the factors of 1742

1,2,13,26,67,134,871,1742

Now, list down the factors of 3662

1,2,1831,3662

Greatest Common Factor

We found the factors 1742,3662 . The biggest common factor number is the GCF number.
So the greatest common factor 1742,3662 is 2.

Lets's calculate LCM of 200,6512

Lowest Common Multiple of 200,6512 using Common Division

2	200, 6512
2	100, 3256
2	50, 1628
	25, 814

∴ So the LCM of the given numbers is 2 x 2 x 2 x 25 x 814 = 162800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/162800

Therefore, the GCF of Fractions 1742/200,3662/6512 is 2/162800

Least Common Multiple of 200,6512 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 200,6512 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(200,6512) = 8

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

GCF(200,6512) x common factors =8 x 1 = 8

LCM(200,6512) = ( 200 × 6512 ) / 8

LCM(200,6512) = 1302400 / 8

LCM(200,6512) = 162800

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FAQs on GCF of Fractions of 1742/200, 3662/6512

1. What is the HCF of 1742,3662?

The HCF of 1742,3662 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 1742/200, 3662/6512?

Answer: GCF of Numerators as per given numbers 1742/200, 3662/6512 is

GCF of Numerators i.e. for 1742,3662 is 2

LCM of denominators i.e. for 200,6512 is 162800.

Thus, GCF of Fractions is 2/162800.Finally, GCF of Fractions for 1742/200, 3662/6512 is 2/162800.