How to Find GCF of 17/420, 47/513, 112/267?

GCF of 17/420, 47/513, 112/267

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 17/420, 47/513, 112/267 i.e 1/6391980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/420, 47/513, 112/267.

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 17/420,47/513,112/267?

Given fractions are 17/420,47/513,112/267

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 17/420,47/513,112/267, numerators are 17,47,112

Denominators are 420,513,267

The GCF of 17,47,112 is 1 .

LCM of 420,513,267 is 6391980.

The greatest common factor of 17/420,47/513,112/267 = [GCF of 17,47,112]/[LCM of 420,513,267]= 1/6391980

Therefore, the GCF of 17/420,47/513,112/267 is 1/6391980.

Greatest Common Factor of 17,47,112

To find the highest common factor of 17,47,112, 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 47 are 1, 47

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

The HCF of 17,47,112 is 1.

Lets's calculate GCF of 17,47,112

Greatest Common Factor (GCF) of 17,47,112 By Common Division

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

Greatest Common Factor of 17,47,112 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 47

1,47

Now, list down the factors of 112

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors 17,47,112 . The biggest common factor number is the GCF number.
So the greatest common factor 17,47,112 is 1.

Lets's calculate LCM of 420,513,267

Lowest Common Multiple of 420,513,267 using Common Division

3	420, 513, 267
	140, 171, 89

∴ So the LCM of the given numbers is 3 x 140 x 171 x 89 = 6391980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6391980

Therefore, the GCF of Fractions 17/420,47/513,112/267 is 1/6391980

Least Common Multiple of 420,513,267 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 420,513,267 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(420,513,267) = 3

common factors(in case of two or more numbers have common factors) = 3

GCF(420,513,267) x common factors =3 x 3 = 9

LCM(420,513,267) = ( 420 × 513 × 267 ) / 9

LCM(420,513,267) = 57527820 / 9

LCM(420,513,267) = 6391980

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FAQs on GCF of Fractions of 17/420, 47/513, 112/267

1. What is the HCF of 17,47,112?

The HCF of 17,47,112 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 17/420, 47/513, 112/267?

Answer: GCF of Numerators as per given numbers 17/420, 47/513, 112/267 is

GCF of Numerators i.e. for 17,47,112 is 1

LCM of denominators i.e. for 420,513,267 is 6391980.

Thus, GCF of Fractions is 1/6391980.Finally, GCF of Fractions for 17/420, 47/513, 112/267 is 1/6391980.