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GCF of 865/42, 513/824

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 865/42, 513/824 i.e 1/17304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 865/42, 513/824.

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 865/42,513/824?

Given fractions are 865/42,513/824

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 865/42,513/824, numerators are 865,513

Denominators are 42,824

The GCF of 865,513 is 1 .

LCM of 42,824 is 17304.

The greatest common factor of 865/42,513/824 = [GCF of 865,513]/[LCM of 42,824]= 1/17304

Therefore, the GCF of 865/42,513/824 is 1/17304.

Greatest Common Factor of 865,513

To find the highest common factor of 865,513, we have to find the factors of both numbers and list the highest common factor.

The factors of 865 are 1, 5, 173, 865

The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513

The HCF of 865,513 is 1.

Lets's calculate GCF of 865,513

Greatest Common Factor (GCF) of 865,513 By Common Division

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

Greatest Common Factor of 865,513 By Matching Biggest Common Factor Method

Greatest Common Factor of 865,513 By Matching Biggest Common Factor Method

Now, list down the factors of 865

:

1,5,173,865

Now, list down the factors of 513

:

1,3,9,19,27,57,171,513

Greatest Common Factor

We found the factors 865,513 . The biggest common factor number is the GCF number.
So the greatest common factor 865,513 is 1.

Lets's calculate LCM of 42,824

Lowest Common Multiple of 42,824 using Common Division

2 42, 824
21, 412

∴ So the LCM of the given numbers is 2 x 21 x 412 = 17304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17304

Therefore, the GCF of Fractions 865/42,513/824 is 1/17304

Least Common Multiple of 42,824 with GCF Formula

Least Common Multiple of 42,824 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 42,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,824) = 2

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

GCF(42,824) x common factors =2 x 1 = 2

LCM(42,824) = ( 42 × 824 ) / 2

LCM(42,824) = 34608 / 2

LCM(42,824) = 17304


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FAQs on GCF of Fractions of 865/42, 513/824

1. What is the HCF of 865,513?

The HCF of 865,513 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 865/42, 513/824?

Answer: GCF of Numerators as per given numbers 865/42, 513/824 is

GCF of Numerators i.e. for 865,513 is 1

LCM of denominators i.e. for 42,824 is 17304.

Thus, GCF of Fractions is 1/17304.Finally, GCF of Fractions for 865/42, 513/824 is 1/17304.