How to Find GCF of 408/195, 1528/1842?

GCF of 408/195, 1528/1842

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 408/195, 1528/1842 i.e 8/119730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/195, 1528/1842.

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 408/195,1528/1842?

Given fractions are 408/195,1528/1842

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 408/195,1528/1842, numerators are 408,1528

Denominators are 195,1842

The GCF of 408,1528 is 8 .

LCM of 195,1842 is 119730.

The greatest common factor of 408/195,1528/1842 = [GCF of 408,1528]/[LCM of 195,1842]= 8/119730

Therefore, the GCF of 408/195,1528/1842 is 8/119730.

Greatest Common Factor of 408,1528

To find the highest common factor of 408,1528, we have to find the factors of both numbers and list the highest common factor.

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

The factors of 1528 are 1, 2, 4, 8, 191, 382, 764, 1528

The HCF of 408,1528 is 8.

Lets's calculate GCF of 408,1528

Greatest Common Factor (GCF) of 408,1528 By Common Division

2	408, 1528
2	204, 764
2	102, 382
	51, 191

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 408,1528 By Matching Biggest Common Factor Method

Now, list down the factors of 408

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Now, list down the factors of 1528

1,2,4,8,191,382,764,1528

Greatest Common Factor

We found the factors 408,1528 . The biggest common factor number is the GCF number.
So the greatest common factor 408,1528 is 8.

Lets's calculate LCM of 195,1842

Lowest Common Multiple of 195,1842 using Common Division

3	195, 1842
	65, 614

∴ So the LCM of the given numbers is 3 x 65 x 614 = 119730

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/119730

Therefore, the GCF of Fractions 408/195,1528/1842 is 8/119730

Least Common Multiple of 195,1842 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 195,1842 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(195,1842) = 3

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

GCF(195,1842) x common factors =3 x 1 = 3

LCM(195,1842) = ( 195 × 1842 ) / 3

LCM(195,1842) = 359190 / 3

LCM(195,1842) = 119730

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FAQs on GCF of Fractions of 408/195, 1528/1842

1. What is the HCF of 408,1528?

The HCF of 408,1528 is 8

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 408/195, 1528/1842?

Answer: GCF of Numerators as per given numbers 408/195, 1528/1842 is

GCF of Numerators i.e. for 408,1528 is 8

LCM of denominators i.e. for 195,1842 is 119730.

Thus, GCF of Fractions is 8/119730.Finally, GCF of Fractions for 408/195, 1528/1842 is 8/119730.