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GCF of 642/538, 407/506

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 642/538, 407/506 i.e 1/136114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/538, 407/506.

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 642/538,407/506?

Given fractions are 642/538,407/506

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 642/538,407/506, numerators are 642,407

Denominators are 538,506

The GCF of 642,407 is 1 .

LCM of 538,506 is 136114.

The greatest common factor of 642/538,407/506 = [GCF of 642,407]/[LCM of 538,506]= 1/136114

Therefore, the GCF of 642/538,407/506 is 1/136114.

Greatest Common Factor of 642,407

To find the highest common factor of 642,407, we have to find the factors of both numbers and list the highest common factor.

The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642

The factors of 407 are 1, 11, 37, 407

The HCF of 642,407 is 1.

Lets's calculate GCF of 642,407

Greatest Common Factor (GCF) of 642,407 By Common Division

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

Greatest Common Factor of 642,407 By Matching Biggest Common Factor Method

Greatest Common Factor of 642,407 By Matching Biggest Common Factor Method

Now, list down the factors of 642

:

1,2,3,6,107,214,321,642

Now, list down the factors of 407

:

1,11,37,407

Greatest Common Factor

We found the factors 642,407 . The biggest common factor number is the GCF number.
So the greatest common factor 642,407 is 1.

Lets's calculate LCM of 538,506

Lowest Common Multiple of 538,506 using Common Division

2 538, 506
269, 253

∴ So the LCM of the given numbers is 2 x 269 x 253 = 136114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/136114

Therefore, the GCF of Fractions 642/538,407/506 is 1/136114

Least Common Multiple of 538,506 with GCF Formula

Least Common Multiple of 538,506 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 538,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(538,506) = 2

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

GCF(538,506) x common factors =2 x 1 = 2

LCM(538,506) = ( 538 × 506 ) / 2

LCM(538,506) = 272228 / 2

LCM(538,506) = 136114


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FAQs on GCF of Fractions of 642/538, 407/506

1. What is the HCF of 642,407?

The HCF of 642,407 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 642/538, 407/506?

Answer: GCF of Numerators as per given numbers 642/538, 407/506 is

GCF of Numerators i.e. for 642,407 is 1

LCM of denominators i.e. for 538,506 is 136114.

Thus, GCF of Fractions is 1/136114.Finally, GCF of Fractions for 642/538, 407/506 is 1/136114.