How to Find GCF of 728/17, 672/8706?

GCF of 728/17, 672/8706

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 728/17, 672/8706 i.e 56/148002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/17, 672/8706.

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 728/17,672/8706?

Given fractions are 728/17,672/8706

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 728/17,672/8706, numerators are 728,672

Denominators are 17,8706

The GCF of 728,672 is 56 .

LCM of 17,8706 is 148002.

The greatest common factor of 728/17,672/8706 = [GCF of 728,672]/[LCM of 17,8706]= 56/148002

Therefore, the GCF of 728/17,672/8706 is 56/148002.

Greatest Common Factor of 728,672

To find the highest common factor of 728,672, we have to find the factors of both numbers and list the highest common factor.

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672

The HCF of 728,672 is 56.

Lets's calculate GCF of 728,672

Greatest Common Factor (GCF) of 728,672 By Common Division

2	728, 672
2	364, 336
2	182, 168
7	91, 84
	13, 12

∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56

Greatest Common Factor of 728,672 By Matching Biggest Common Factor Method

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Now, list down the factors of 672

1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672

Greatest Common Factor

We found the factors 728,672 . The biggest common factor number is the GCF number.
So the greatest common factor 728,672 is 56.

Lets's calculate LCM of 17,8706

Lowest Common Multiple of 17,8706 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 148002

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/148002

Therefore, the GCF of Fractions 728/17,672/8706 is 56/148002

Least Common Multiple of 17,8706 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 17,8706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,8706) = 1

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

GCF(17,8706) x common factors =1 x 1 = 1

LCM(17,8706) = ( 17 × 8706 ) / 1

LCM(17,8706) = 148002 / 1

LCM(17,8706) = 148002

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FAQs on GCF of Fractions of 728/17, 672/8706

1. What is the HCF of 728,672?

The HCF of 728,672 is 56

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 728/17, 672/8706?

Answer: GCF of Numerators as per given numbers 728/17, 672/8706 is

GCF of Numerators i.e. for 728,672 is 56

LCM of denominators i.e. for 17,8706 is 148002.

Thus, GCF of Fractions is 56/148002.Finally, GCF of Fractions for 728/17, 672/8706 is 56/148002.