How to Find GCF of 51/272, 13/414, 667/332?

GCF of 51/272, 13/414, 667/332

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 51/272, 13/414, 667/332 i.e 1/4673232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/272, 13/414, 667/332.

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 51/272,13/414,667/332?

Given fractions are 51/272,13/414,667/332

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 51/272,13/414,667/332, numerators are 51,13,667

Denominators are 272,414,332

The GCF of 51,13,667 is 1 .

LCM of 272,414,332 is 4673232.

The greatest common factor of 51/272,13/414,667/332 = [GCF of 51,13,667]/[LCM of 272,414,332]= 1/4673232

Therefore, the GCF of 51/272,13/414,667/332 is 1/4673232.

Greatest Common Factor of 51,13,667

To find the highest common factor of 51,13,667, we have to find the factors of both numbers and list the highest common factor.

The factors of 51 are 1, 3, 17, 51

The factors of 13 are 1, 13

The factors of 667 are 1, 23, 29, 667

The HCF of 51,13,667 is 1.

Lets's calculate GCF of 51,13,667

Greatest Common Factor (GCF) of 51,13,667 By Common Division

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

Greatest Common Factor of 51,13,667 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 13

1,13

Now, list down the factors of 667

1,23,29,667

Greatest Common Factor

We found the factors 51,13,667 . The biggest common factor number is the GCF number.
So the greatest common factor 51,13,667 is 1.

Lets's calculate LCM of 272,414,332

Lowest Common Multiple of 272,414,332 using Common Division

2	272, 414, 332
2	136, 207, 166
	68, 207, 83

∴ So the LCM of the given numbers is 2 x 2 x 68 x 207 x 83 = 4673232

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4673232

Therefore, the GCF of Fractions 51/272,13/414,667/332 is 1/4673232

Least Common Multiple of 272,414,332 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 272,414,332 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(272,414,332) = 2

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

GCF(272,414,332) x common factors =2 x 4 = 8

LCM(272,414,332) = ( 272 × 414 × 332 ) / 8

LCM(272,414,332) = 37385856 / 8

LCM(272,414,332) = 4673232

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FAQs on GCF of Fractions of 51/272, 13/414, 667/332

1. What is the HCF of 51,13,667?

The HCF of 51,13,667 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 51/272, 13/414, 667/332?

Answer: GCF of Numerators as per given numbers 51/272, 13/414, 667/332 is

GCF of Numerators i.e. for 51,13,667 is 1

LCM of denominators i.e. for 272,414,332 is 4673232.

Thus, GCF of Fractions is 1/4673232.Finally, GCF of Fractions for 51/272, 13/414, 667/332 is 1/4673232.