How to Find GCF of 1667/400, 5445/3200?

GCF of 1667/400, 5445/3200

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 1667/400, 5445/3200 i.e 1/3200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1667/400, 5445/3200.

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 1667/400,5445/3200?

Given fractions are 1667/400,5445/3200

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 1667/400,5445/3200, numerators are 1667,5445

Denominators are 400,3200

The GCF of 1667,5445 is 1 .

LCM of 400,3200 is 3200.

The greatest common factor of 1667/400,5445/3200 = [GCF of 1667,5445]/[LCM of 400,3200]= 1/3200

Therefore, the GCF of 1667/400,5445/3200 is 1/3200.

Greatest Common Factor of 1667,5445

To find the highest common factor of 1667,5445, we have to find the factors of both numbers and list the highest common factor.

The factors of 1667 are 1, 1667

The factors of 5445 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 121, 165, 363, 495, 605, 1089, 1815, 5445

The HCF of 1667,5445 is 1.

Lets's calculate GCF of 1667,5445

Greatest Common Factor (GCF) of 1667,5445 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 1667,5445 By Matching Biggest Common Factor Method

Now, list down the factors of 1667

1,1667

Now, list down the factors of 5445

1,3,5,9,11,15,33,45,55,99,121,165,363,495,605,1089,1815,5445

Greatest Common Factor

We found the factors 1667,5445 . The biggest common factor number is the GCF number.
So the greatest common factor 1667,5445 is 1.

Lets's calculate LCM of 400,3200

Lowest Common Multiple of 400,3200 using Common Division

2	400, 3200
2	200, 1600
2	100, 800
2	50, 400
5	25, 200
5	5, 40
	1, 8

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 5 x 1 x 8 = 3200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3200

Therefore, the GCF of Fractions 1667/400,5445/3200 is 1/3200

Least Common Multiple of 400,3200 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 400,3200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,3200) = 400

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

GCF(400,3200) x common factors =400 x 1 = 400

LCM(400,3200) = ( 400 × 3200 ) / 400

LCM(400,3200) = 1280000 / 400

LCM(400,3200) = 3200

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1667/400, 5445/3200

1. What is the HCF of 1667,5445?

The HCF of 1667,5445 is 1

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 1667/400, 5445/3200?

Answer: GCF of Numerators as per given numbers 1667/400, 5445/3200 is

GCF of Numerators i.e. for 1667,5445 is 1

LCM of denominators i.e. for 400,3200 is 3200.

Thus, GCF of Fractions is 1/3200.Finally, GCF of Fractions for 1667/400, 5445/3200 is 1/3200.