How to Find GCF of 132/26, 817/37, 407/19?

GCF of 132/26, 817/37, 407/19

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 132/26, 817/37, 407/19 i.e 1/18278 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/26, 817/37, 407/19.

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 132/26,817/37,407/19?

Given fractions are 132/26,817/37,407/19

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 132/26,817/37,407/19, numerators are 132,817,407

Denominators are 26,37,19

The GCF of 132,817,407 is 1 .

LCM of 26,37,19 is 18278.

The greatest common factor of 132/26,817/37,407/19 = [GCF of 132,817,407]/[LCM of 26,37,19]= 1/18278

Therefore, the GCF of 132/26,817/37,407/19 is 1/18278.

Greatest Common Factor of 132,817,407

To find the highest common factor of 132,817,407, we have to find the factors of both numbers and list the highest common factor.

The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

The factors of 817 are 1, 19, 43, 817

The factors of 407 are 1, 11, 37, 407

The HCF of 132,817,407 is 1.

Lets's calculate GCF of 132,817,407

Greatest Common Factor (GCF) of 132,817,407 By Common Division

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

Greatest Common Factor of 132,817,407 By Matching Biggest Common Factor Method

Now, list down the factors of 132

1,2,3,4,6,11,12,22,33,44,66,132

Now, list down the factors of 817

1,19,43,817

Now, list down the factors of 407

1,11,37,407

Greatest Common Factor

We found the factors 132,817,407 . The biggest common factor number is the GCF number.
So the greatest common factor 132,817,407 is 1.

Lets's calculate LCM of 26,37,19

Lowest Common Multiple of 26,37,19 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 18278

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18278

Therefore, the GCF of Fractions 132/26,817/37,407/19 is 1/18278

Least Common Multiple of 26,37,19 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 26,37,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,37,19) = 1

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

GCF(26,37,19) x common factors =1 x 1 = 1

LCM(26,37,19) = ( 26 × 37 × 19 ) / 1

LCM(26,37,19) = 18278 / 1

LCM(26,37,19) = 18278

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FAQs on GCF of Fractions of 132/26, 817/37, 407/19

1. What is the HCF of 132,817,407?

The HCF of 132,817,407 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 132/26, 817/37, 407/19?

Answer: GCF of Numerators as per given numbers 132/26, 817/37, 407/19 is

GCF of Numerators i.e. for 132,817,407 is 1

LCM of denominators i.e. for 26,37,19 is 18278.

Thus, GCF of Fractions is 1/18278.Finally, GCF of Fractions for 132/26, 817/37, 407/19 is 1/18278.