How to Find GCF of 826/649, 828/729?

GCF of 826/649, 828/729

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 826/649, 828/729 i.e 2/473121 easily. The following is the detailed procedure to determine the greatest common factor of fractions 826/649, 828/729.

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 826/649,828/729?

Given fractions are 826/649,828/729

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 826/649,828/729, numerators are 826,828

Denominators are 649,729

The GCF of 826,828 is 2 .

LCM of 649,729 is 473121.

The greatest common factor of 826/649,828/729 = [GCF of 826,828]/[LCM of 649,729]= 2/473121

Therefore, the GCF of 826/649,828/729 is 2/473121.

Greatest Common Factor of 826,828

To find the highest common factor of 826,828, we have to find the factors of both numbers and list the highest common factor.

The factors of 826 are 1, 2, 7, 14, 59, 118, 413, 826

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

The HCF of 826,828 is 2.

Lets's calculate GCF of 826,828

Greatest Common Factor (GCF) of 826,828 By Common Division

2	826, 828
	413, 414

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

Greatest Common Factor of 826,828 By Matching Biggest Common Factor Method

Now, list down the factors of 826

1,2,7,14,59,118,413,826

Now, list down the factors of 828

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors 826,828 . The biggest common factor number is the GCF number.
So the greatest common factor 826,828 is 2.

Lets's calculate LCM of 649,729

Lowest Common Multiple of 649,729 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 473121

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/473121

Therefore, the GCF of Fractions 826/649,828/729 is 2/473121

Least Common Multiple of 649,729 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 649,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(649,729) = 1

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

GCF(649,729) x common factors =1 x 1 = 1

LCM(649,729) = ( 649 × 729 ) / 1

LCM(649,729) = 473121 / 1

LCM(649,729) = 473121

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FAQs on GCF of Fractions of 826/649, 828/729

1. What is the HCF of 826,828?

The HCF of 826,828 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 826/649, 828/729?

Answer: GCF of Numerators as per given numbers 826/649, 828/729 is

GCF of Numerators i.e. for 826,828 is 2

LCM of denominators i.e. for 649,729 is 473121.

Thus, GCF of Fractions is 2/473121.Finally, GCF of Fractions for 826/649, 828/729 is 2/473121.