How to Find GCF of 462/287, 5438/3678?

GCF of 462/287, 5438/3678

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 462/287, 5438/3678 i.e 2/1055586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/287, 5438/3678.

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 462/287,5438/3678?

Given fractions are 462/287,5438/3678

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 462/287,5438/3678, numerators are 462,5438

Denominators are 287,3678

The GCF of 462,5438 is 2 .

LCM of 287,3678 is 1055586.

The greatest common factor of 462/287,5438/3678 = [GCF of 462,5438]/[LCM of 287,3678]= 2/1055586

Therefore, the GCF of 462/287,5438/3678 is 2/1055586.

Greatest Common Factor of 462,5438

To find the highest common factor of 462,5438, we have to find the factors of both numbers and list the highest common factor.

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

The factors of 5438 are 1, 2, 2719, 5438

The HCF of 462,5438 is 2.

Lets's calculate GCF of 462,5438

Greatest Common Factor (GCF) of 462,5438 By Common Division

2	462, 5438
	231, 2719

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

Greatest Common Factor of 462,5438 By Matching Biggest Common Factor Method

Now, list down the factors of 462

1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462

Now, list down the factors of 5438

1,2,2719,5438

Greatest Common Factor

We found the factors 462,5438 . The biggest common factor number is the GCF number.
So the greatest common factor 462,5438 is 2.

Lets's calculate LCM of 287,3678

Lowest Common Multiple of 287,3678 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1055586

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1055586

Therefore, the GCF of Fractions 462/287,5438/3678 is 2/1055586

Least Common Multiple of 287,3678 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 287,3678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(287,3678) = 1

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

GCF(287,3678) x common factors =1 x 1 = 1

LCM(287,3678) = ( 287 × 3678 ) / 1

LCM(287,3678) = 1055586 / 1

LCM(287,3678) = 1055586

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FAQs on GCF of Fractions of 462/287, 5438/3678

1. What is the HCF of 462,5438?

The HCF of 462,5438 is 2

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 462/287, 5438/3678?

Answer: GCF of Numerators as per given numbers 462/287, 5438/3678 is

GCF of Numerators i.e. for 462,5438 is 2

LCM of denominators i.e. for 287,3678 is 1055586.

Thus, GCF of Fractions is 2/1055586.Finally, GCF of Fractions for 462/287, 5438/3678 is 2/1055586.