How to Find GCF of 408/67, 872/166?

GCF of 408/67, 872/166

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 408/67, 872/166 i.e 8/11122 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/67, 872/166.

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 408/67,872/166?

Given fractions are 408/67,872/166

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 408/67,872/166, numerators are 408,872

Denominators are 67,166

The GCF of 408,872 is 8 .

LCM of 67,166 is 11122.

The greatest common factor of 408/67,872/166 = [GCF of 408,872]/[LCM of 67,166]= 8/11122

Therefore, the GCF of 408/67,872/166 is 8/11122.

Greatest Common Factor of 408,872

To find the highest common factor of 408,872, 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 872 are 1, 2, 4, 8, 109, 218, 436, 872

The HCF of 408,872 is 8.

Lets's calculate GCF of 408,872

Greatest Common Factor (GCF) of 408,872 By Common Division

2	408, 872
2	204, 436
2	102, 218
	51, 109

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

Greatest Common Factor of 408,872 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 872

1,2,4,8,109,218,436,872

Greatest Common Factor

We found the factors 408,872 . The biggest common factor number is the GCF number.
So the greatest common factor 408,872 is 8.

Lets's calculate LCM of 67,166

Lowest Common Multiple of 67,166 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11122

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/11122

Therefore, the GCF of Fractions 408/67,872/166 is 8/11122

Least Common Multiple of 67,166 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 67,166 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,166) = 1

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

GCF(67,166) x common factors =1 x 1 = 1

LCM(67,166) = ( 67 × 166 ) / 1

LCM(67,166) = 11122 / 1

LCM(67,166) = 11122

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FAQs on GCF of Fractions of 408/67, 872/166

1. What is the HCF of 408,872?

The HCF of 408,872 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 408/67, 872/166?

Answer: GCF of Numerators as per given numbers 408/67, 872/166 is

GCF of Numerators i.e. for 408,872 is 8

LCM of denominators i.e. for 67,166 is 11122.

Thus, GCF of Fractions is 8/11122.Finally, GCF of Fractions for 408/67, 872/166 is 8/11122.