How to Find GCF of 828/53, 940/361?

GCF of 828/53, 940/361

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 828/53, 940/361 i.e 4/19133 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/53, 940/361.

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 828/53,940/361?

Given fractions are 828/53,940/361

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 828/53,940/361, numerators are 828,940

Denominators are 53,361

The GCF of 828,940 is 4 .

LCM of 53,361 is 19133.

The greatest common factor of 828/53,940/361 = [GCF of 828,940]/[LCM of 53,361]= 4/19133

Therefore, the GCF of 828/53,940/361 is 4/19133.

Greatest Common Factor of 828,940

To find the highest common factor of 828,940, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 940 are 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940

The HCF of 828,940 is 4.

Lets's calculate GCF of 828,940

Greatest Common Factor (GCF) of 828,940 By Common Division

2	828, 940
2	414, 470
	207, 235

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

Greatest Common Factor of 828,940 By Matching Biggest Common Factor Method

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

Now, list down the factors of 940

1,2,4,5,10,20,47,94,188,235,470,940

Greatest Common Factor

We found the factors 828,940 . The biggest common factor number is the GCF number.
So the greatest common factor 828,940 is 4.

Lets's calculate LCM of 53,361

Lowest Common Multiple of 53,361 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 19133

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/19133

Therefore, the GCF of Fractions 828/53,940/361 is 4/19133

Least Common Multiple of 53,361 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 53,361 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(53,361) = 1

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

GCF(53,361) x common factors =1 x 1 = 1

LCM(53,361) = ( 53 × 361 ) / 1

LCM(53,361) = 19133 / 1

LCM(53,361) = 19133

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FAQs on GCF of Fractions of 828/53, 940/361

1. What is the HCF of 828,940?

The HCF of 828,940 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 828/53, 940/361?

Answer: GCF of Numerators as per given numbers 828/53, 940/361 is

GCF of Numerators i.e. for 828,940 is 4

LCM of denominators i.e. for 53,361 is 19133.

Thus, GCF of Fractions is 4/19133.Finally, GCF of Fractions for 828/53, 940/361 is 4/19133.