How to Find GCF of 546/456, 8173/896?

GCF of 546/456, 8173/896

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 546/456, 8173/896 i.e 1/51072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/456, 8173/896.

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 546/456,8173/896?

Given fractions are 546/456,8173/896

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 546/456,8173/896, numerators are 546,8173

Denominators are 456,896

The GCF of 546,8173 is 1 .

LCM of 456,896 is 51072.

The greatest common factor of 546/456,8173/896 = [GCF of 546,8173]/[LCM of 456,896]= 1/51072

Therefore, the GCF of 546/456,8173/896 is 1/51072.

Greatest Common Factor of 546,8173

To find the highest common factor of 546,8173, we have to find the factors of both numbers and list the highest common factor.

The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546

The factors of 8173 are 1, 11, 743, 8173

The HCF of 546,8173 is 1.

Lets's calculate GCF of 546,8173

Greatest Common Factor (GCF) of 546,8173 By Common Division

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

Greatest Common Factor of 546,8173 By Matching Biggest Common Factor Method

Now, list down the factors of 546

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Now, list down the factors of 8173

1,11,743,8173

Greatest Common Factor

We found the factors 546,8173 . The biggest common factor number is the GCF number.
So the greatest common factor 546,8173 is 1.

Lets's calculate LCM of 456,896

Lowest Common Multiple of 456,896 using Common Division

2	456, 896
2	228, 448
2	114, 224
	57, 112

∴ So the LCM of the given numbers is 2 x 2 x 2 x 57 x 112 = 51072

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51072

Therefore, the GCF of Fractions 546/456,8173/896 is 1/51072

Least Common Multiple of 456,896 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 456,896 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(456,896) = 8

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

GCF(456,896) x common factors =8 x 1 = 8

LCM(456,896) = ( 456 × 896 ) / 8

LCM(456,896) = 408576 / 8

LCM(456,896) = 51072

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FAQs on GCF of Fractions of 546/456, 8173/896

1. What is the HCF of 546,8173?

The HCF of 546,8173 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 546/456, 8173/896?

Answer: GCF of Numerators as per given numbers 546/456, 8173/896 is

GCF of Numerators i.e. for 546,8173 is 1

LCM of denominators i.e. for 456,896 is 51072.

Thus, GCF of Fractions is 1/51072.Finally, GCF of Fractions for 546/456, 8173/896 is 1/51072.