How to Find GCF of 408/463, 3126/137?

GCF of 408/463, 3126/137

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 408/463, 3126/137 i.e 6/63431 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/463, 3126/137.

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 408/463,3126/137?

Given fractions are 408/463,3126/137

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 408/463,3126/137, numerators are 408,3126

Denominators are 463,137

The GCF of 408,3126 is 6 .

LCM of 463,137 is 63431.

The greatest common factor of 408/463,3126/137 = [GCF of 408,3126]/[LCM of 463,137]= 6/63431

Therefore, the GCF of 408/463,3126/137 is 6/63431.

Greatest Common Factor of 408,3126

To find the highest common factor of 408,3126, 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 3126 are 1, 2, 3, 6, 521, 1042, 1563, 3126

The HCF of 408,3126 is 6.

Lets's calculate GCF of 408,3126

Greatest Common Factor (GCF) of 408,3126 By Common Division

2	408, 3126
3	204, 1563
	68, 521

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 408,3126 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 3126

1,2,3,6,521,1042,1563,3126

Greatest Common Factor

We found the factors 408,3126 . The biggest common factor number is the GCF number.
So the greatest common factor 408,3126 is 6.

Lets's calculate LCM of 463,137

Lowest Common Multiple of 463,137 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 63431

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/63431

Therefore, the GCF of Fractions 408/463,3126/137 is 6/63431

Least Common Multiple of 463,137 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 463,137 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(463,137) = 1

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

GCF(463,137) x common factors =1 x 1 = 1

LCM(463,137) = ( 463 × 137 ) / 1

LCM(463,137) = 63431 / 1

LCM(463,137) = 63431

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FAQs on GCF of Fractions of 408/463, 3126/137

1. What is the HCF of 408,3126?

The HCF of 408,3126 is 6

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 408/463, 3126/137?

Answer: GCF of Numerators as per given numbers 408/463, 3126/137 is

GCF of Numerators i.e. for 408,3126 is 6

LCM of denominators i.e. for 463,137 is 63431.

Thus, GCF of Fractions is 6/63431.Finally, GCF of Fractions for 408/463, 3126/137 is 6/63431.