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GCF of 412/65, 460/4937

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 412/65, 460/4937 i.e 4/320905 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/65, 460/4937.

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 412/65,460/4937?

Given fractions are 412/65,460/4937

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 412/65,460/4937, numerators are 412,460

Denominators are 65,4937

The GCF of 412,460 is 4 .

LCM of 65,4937 is 320905.

The greatest common factor of 412/65,460/4937 = [GCF of 412,460]/[LCM of 65,4937]= 4/320905

Therefore, the GCF of 412/65,460/4937 is 4/320905.

Greatest Common Factor of 412,460

To find the highest common factor of 412,460, we have to find the factors of both numbers and list the highest common factor.

The factors of 412 are 1, 2, 4, 103, 206, 412

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

The HCF of 412,460 is 4.

Lets's calculate GCF of 412,460

Greatest Common Factor (GCF) of 412,460 By Common Division

2 412, 460
2 206, 230
103, 115

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 412,460 By Matching Biggest Common Factor Method

Greatest Common Factor of 412,460 By Matching Biggest Common Factor Method

Now, list down the factors of 412

:

1,2,4,103,206,412

Now, list down the factors of 460

:

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors 412,460 . The biggest common factor number is the GCF number.
So the greatest common factor 412,460 is 4.

Lets's calculate LCM of 65,4937

Lowest Common Multiple of 65,4937 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 320905

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/320905

Therefore, the GCF of Fractions 412/65,460/4937 is 4/320905

Least Common Multiple of 65,4937 with GCF Formula

Least Common Multiple of 65,4937 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 65,4937 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,4937) = 1

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

GCF(65,4937) x common factors =1 x 1 = 1

LCM(65,4937) = ( 65 × 4937 ) / 1

LCM(65,4937) = 320905 / 1

LCM(65,4937) = 320905


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FAQs on GCF of Fractions of 412/65, 460/4937

1. What is the HCF of 412,460?

The HCF of 412,460 is 4

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 412/65, 460/4937?

Answer: GCF of Numerators as per given numbers 412/65, 460/4937 is

GCF of Numerators i.e. for 412,460 is 4

LCM of denominators i.e. for 65,4937 is 320905.

Thus, GCF of Fractions is 4/320905.Finally, GCF of Fractions for 412/65, 460/4937 is 4/320905.