How to Find GCF of 87/39, 34/31, 162/24?

GCF of 87/39, 34/31, 162/24

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 87/39, 34/31, 162/24 i.e 1/9672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/39, 34/31, 162/24.

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 87/39,34/31,162/24?

Given fractions are 87/39,34/31,162/24

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 87/39,34/31,162/24, numerators are 87,34,162

Denominators are 39,31,24

The GCF of 87,34,162 is 1 .

LCM of 39,31,24 is 9672.

The greatest common factor of 87/39,34/31,162/24 = [GCF of 87,34,162]/[LCM of 39,31,24]= 1/9672

Therefore, the GCF of 87/39,34/31,162/24 is 1/9672.

Greatest Common Factor of 87,34,162

To find the highest common factor of 87,34,162, we have to find the factors of both numbers and list the highest common factor.

The factors of 87 are 1, 3, 29, 87

The factors of 34 are 1, 2, 17, 34

The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162

The HCF of 87,34,162 is 1.

Lets's calculate GCF of 87,34,162

Greatest Common Factor (GCF) of 87,34,162 By Common Division

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

Greatest Common Factor of 87,34,162 By Matching Biggest Common Factor Method

Now, list down the factors of 87

1,3,29,87

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 162

1,2,3,6,9,18,27,54,81,162

Greatest Common Factor

We found the factors 87,34,162 . The biggest common factor number is the GCF number.
So the greatest common factor 87,34,162 is 1.

Lets's calculate LCM of 39,31,24

Lowest Common Multiple of 39,31,24 using Common Division

3	39, 31, 24
	13, 31, 8

∴ So the LCM of the given numbers is 3 x 13 x 31 x 8 = 9672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9672

Therefore, the GCF of Fractions 87/39,34/31,162/24 is 1/9672

Least Common Multiple of 39,31,24 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 39,31,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(39,31,24) = 1

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

GCF(39,31,24) x common factors =1 x 3 = 3

LCM(39,31,24) = ( 39 × 31 × 24 ) / 3

LCM(39,31,24) = 29016 / 3

LCM(39,31,24) = 9672

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FAQs on GCF of Fractions of 87/39, 34/31, 162/24

1. What is the HCF of 87,34,162?

The HCF of 87,34,162 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 87/39, 34/31, 162/24?

Answer: GCF of Numerators as per given numbers 87/39, 34/31, 162/24 is

GCF of Numerators i.e. for 87,34,162 is 1

LCM of denominators i.e. for 39,31,24 is 9672.

Thus, GCF of Fractions is 1/9672.Finally, GCF of Fractions for 87/39, 34/31, 162/24 is 1/9672.