How to Find GCF of 17/284, 31/716, 100/751?

GCF of 17/284, 31/716, 100/751

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 17/284, 31/716, 100/751 i.e 1/38177836 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/284, 31/716, 100/751.

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 17/284,31/716,100/751?

Given fractions are 17/284,31/716,100/751

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 17/284,31/716,100/751, numerators are 17,31,100

Denominators are 284,716,751

The GCF of 17,31,100 is 1 .

LCM of 284,716,751 is 38177836.

The greatest common factor of 17/284,31/716,100/751 = [GCF of 17,31,100]/[LCM of 284,716,751]= 1/38177836

Therefore, the GCF of 17/284,31/716,100/751 is 1/38177836.

Greatest Common Factor of 17,31,100

To find the highest common factor of 17,31,100, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 31 are 1, 31

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100

The HCF of 17,31,100 is 1.

Lets's calculate GCF of 17,31,100

Greatest Common Factor (GCF) of 17,31,100 By Common Division

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

Greatest Common Factor of 17,31,100 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 31

1,31

Now, list down the factors of 100

1,2,4,5,10,20,25,50,100

Greatest Common Factor

We found the factors 17,31,100 . The biggest common factor number is the GCF number.
So the greatest common factor 17,31,100 is 1.

Lets's calculate LCM of 284,716,751

Lowest Common Multiple of 284,716,751 using Common Division

2	284, 716, 751
2	142, 358, 751
	71, 179, 751

∴ So the LCM of the given numbers is 2 x 2 x 71 x 179 x 751 = 38177836

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38177836

Therefore, the GCF of Fractions 17/284,31/716,100/751 is 1/38177836

Least Common Multiple of 284,716,751 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 284,716,751 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,716,751) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(284,716,751) x common factors =1 x 4 = 4

LCM(284,716,751) = ( 284 × 716 × 751 ) / 4

LCM(284,716,751) = 152711344 / 4

LCM(284,716,751) = 38177836

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/284, 31/716, 100/751

1. What is the HCF of 17,31,100?

The HCF of 17,31,100 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 17/284, 31/716, 100/751?

Answer: GCF of Numerators as per given numbers 17/284, 31/716, 100/751 is

GCF of Numerators i.e. for 17,31,100 is 1

LCM of denominators i.e. for 284,716,751 is 38177836.

Thus, GCF of Fractions is 1/38177836.Finally, GCF of Fractions for 17/284, 31/716, 100/751 is 1/38177836.