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GCF of 462/380, 463/576

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 462/380, 463/576 i.e 1/54720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/380, 463/576.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 462/380,463/576?

Given fractions are 462/380,463/576

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 462/380,463/576, numerators are 462,463

Denominators are 380,576

The GCF of 462,463 is 1 .

LCM of 380,576 is 54720.

The greatest common factor of 462/380,463/576 = [GCF of 462,463]/[LCM of 380,576]= 1/54720

Therefore, the GCF of 462/380,463/576 is 1/54720.

Greatest Common Factor of 462,463

To find the highest common factor of 462,463, 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 463 are 1, 463

The HCF of 462,463 is 1.

Lets's calculate GCF of 462,463

Greatest Common Factor (GCF) of 462,463 By Common Division

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

Greatest Common Factor of 462,463 By Matching Biggest Common Factor Method

Greatest Common Factor of 462,463 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 463

:

1,463

Greatest Common Factor

We found the factors 462,463 . The biggest common factor number is the GCF number.
So the greatest common factor 462,463 is 1.

Lets's calculate LCM of 380,576

Lowest Common Multiple of 380,576 using Common Division

2 380, 576
2 190, 288
95, 144

∴ So the LCM of the given numbers is 2 x 2 x 95 x 144 = 54720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/54720

Therefore, the GCF of Fractions 462/380,463/576 is 1/54720

Least Common Multiple of 380,576 with GCF Formula

Least Common Multiple of 380,576 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 380,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(380,576) = 4

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

GCF(380,576) x common factors =4 x 1 = 4

LCM(380,576) = ( 380 × 576 ) / 4

LCM(380,576) = 218880 / 4

LCM(380,576) = 54720


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FAQs on GCF of Fractions of 462/380, 463/576

1. What is the HCF of 462,463?

The HCF of 462,463 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 462/380, 463/576?

Answer: GCF of Numerators as per given numbers 462/380, 463/576 is

GCF of Numerators i.e. for 462,463 is 1

LCM of denominators i.e. for 380,576 is 54720.

Thus, GCF of Fractions is 1/54720.Finally, GCF of Fractions for 462/380, 463/576 is 1/54720.