How to Find GCF of 1969/480, 1805/6730?

GCF of 1969/480, 1805/6730

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 1969/480, 1805/6730 i.e 1/323040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1969/480, 1805/6730.

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 1969/480,1805/6730?

Given fractions are 1969/480,1805/6730

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 1969/480,1805/6730, numerators are 1969,1805

Denominators are 480,6730

The GCF of 1969,1805 is 1 .

LCM of 480,6730 is 323040.

The greatest common factor of 1969/480,1805/6730 = [GCF of 1969,1805]/[LCM of 480,6730]= 1/323040

Therefore, the GCF of 1969/480,1805/6730 is 1/323040.

Greatest Common Factor of 1969,1805

To find the highest common factor of 1969,1805, we have to find the factors of both numbers and list the highest common factor.

The factors of 1969 are 1, 11, 179, 1969

The factors of 1805 are 1, 5, 19, 95, 361, 1805

The HCF of 1969,1805 is 1.

Lets's calculate GCF of 1969,1805

Greatest Common Factor (GCF) of 1969,1805 By Common Division

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

Greatest Common Factor of 1969,1805 By Matching Biggest Common Factor Method

Now, list down the factors of 1969

1,11,179,1969

Now, list down the factors of 1805

1,5,19,95,361,1805

Greatest Common Factor

We found the factors 1969,1805 . The biggest common factor number is the GCF number.
So the greatest common factor 1969,1805 is 1.

Lets's calculate LCM of 480,6730

Lowest Common Multiple of 480,6730 using Common Division

2	480, 6730
5	240, 3365
	48, 673

∴ So the LCM of the given numbers is 2 x 5 x 48 x 673 = 323040

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/323040

Therefore, the GCF of Fractions 1969/480,1805/6730 is 1/323040

Least Common Multiple of 480,6730 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 480,6730 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(480,6730) = 10

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

GCF(480,6730) x common factors =10 x 1 = 10

LCM(480,6730) = ( 480 × 6730 ) / 10

LCM(480,6730) = 3230400 / 10

LCM(480,6730) = 323040

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FAQs on GCF of Fractions of 1969/480, 1805/6730

1. What is the HCF of 1969,1805?

The HCF of 1969,1805 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 1969/480, 1805/6730?

Answer: GCF of Numerators as per given numbers 1969/480, 1805/6730 is

GCF of Numerators i.e. for 1969,1805 is 1

LCM of denominators i.e. for 480,6730 is 323040.

Thus, GCF of Fractions is 1/323040.Finally, GCF of Fractions for 1969/480, 1805/6730 is 1/323040.