How to Find GCF of 416/654, 884/973?

GCF of 416/654, 884/973

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 416/654, 884/973 i.e 52/636342 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/654, 884/973.

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 416/654,884/973?

Given fractions are 416/654,884/973

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 416/654,884/973, numerators are 416,884

Denominators are 654,973

The GCF of 416,884 is 52 .

LCM of 654,973 is 636342.

The greatest common factor of 416/654,884/973 = [GCF of 416,884]/[LCM of 654,973]= 52/636342

Therefore, the GCF of 416/654,884/973 is 52/636342.

Greatest Common Factor of 416,884

To find the highest common factor of 416,884, we have to find the factors of both numbers and list the highest common factor.

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The factors of 884 are 1, 2, 4, 13, 17, 26, 34, 52, 68, 221, 442, 884

The HCF of 416,884 is 52.

Lets's calculate GCF of 416,884

Greatest Common Factor (GCF) of 416,884 By Common Division

2	416, 884
2	208, 442
13	104, 221
	8, 17

∴ So the GCF of the given numbers is 2 x 2 x 13 = 52

Greatest Common Factor of 416,884 By Matching Biggest Common Factor Method

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

Now, list down the factors of 884

1,2,4,13,17,26,34,52,68,221,442,884

Greatest Common Factor

We found the factors 416,884 . The biggest common factor number is the GCF number.
So the greatest common factor 416,884 is 52.

Lets's calculate LCM of 654,973

Lowest Common Multiple of 654,973 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 636342

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 52/636342

Therefore, the GCF of Fractions 416/654,884/973 is 52/636342

Least Common Multiple of 654,973 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 654,973 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(654,973) = 1

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

GCF(654,973) x common factors =1 x 1 = 1

LCM(654,973) = ( 654 × 973 ) / 1

LCM(654,973) = 636342 / 1

LCM(654,973) = 636342

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FAQs on GCF of Fractions of 416/654, 884/973

1. What is the HCF of 416,884?

The HCF of 416,884 is 52

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 416/654, 884/973?

Answer: GCF of Numerators as per given numbers 416/654, 884/973 is

GCF of Numerators i.e. for 416,884 is 52

LCM of denominators i.e. for 654,973 is 636342.

Thus, GCF of Fractions is 52/636342.Finally, GCF of Fractions for 416/654, 884/973 is 52/636342.