How to Find GCF of 89/68, 69/90, 31/36?

GCF of 89/68, 69/90, 31/36

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 89/68, 69/90, 31/36 i.e 1/3060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 89/68, 69/90, 31/36.

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 89/68,69/90,31/36?

Given fractions are 89/68,69/90,31/36

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 89/68,69/90,31/36, numerators are 89,69,31

Denominators are 68,90,36

The GCF of 89,69,31 is 1 .

LCM of 68,90,36 is 3060.

The greatest common factor of 89/68,69/90,31/36 = [GCF of 89,69,31]/[LCM of 68,90,36]= 1/3060

Therefore, the GCF of 89/68,69/90,31/36 is 1/3060.

Greatest Common Factor of 89,69,31

To find the highest common factor of 89,69,31, we have to find the factors of both numbers and list the highest common factor.

The factors of 89 are 1, 89

The factors of 69 are 1, 3, 23, 69

The factors of 31 are 1, 31

The HCF of 89,69,31 is 1.

Lets's calculate GCF of 89,69,31

Greatest Common Factor (GCF) of 89,69,31 By Common Division

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

Greatest Common Factor of 89,69,31 By Matching Biggest Common Factor Method

Now, list down the factors of 89

1,89

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 31

1,31

Greatest Common Factor

We found the factors 89,69,31 . The biggest common factor number is the GCF number.
So the greatest common factor 89,69,31 is 1.

Lets's calculate LCM of 68,90,36

Lowest Common Multiple of 68,90,36 using Common Division

2	68, 90, 36
2	34, 45, 18
3	17, 45, 9
3	17, 15, 3
	17, 5, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 17 x 5 x 1 = 3060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3060

Therefore, the GCF of Fractions 89/68,69/90,31/36 is 1/3060

Least Common Multiple of 68,90,36 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 68,90,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,90,36) = 2

common factors(in case of two or more numbers have common factors) = 36

GCF(68,90,36) x common factors =2 x 36 = 72

LCM(68,90,36) = ( 68 × 90 × 36 ) / 72

LCM(68,90,36) = 220320 / 72

LCM(68,90,36) = 3060

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FAQs on GCF of Fractions of 89/68, 69/90, 31/36

1. What is the HCF of 89,69,31?

The HCF of 89,69,31 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 89/68, 69/90, 31/36?

Answer: GCF of Numerators as per given numbers 89/68, 69/90, 31/36 is

GCF of Numerators i.e. for 89,69,31 is 1

LCM of denominators i.e. for 68,90,36 is 3060.

Thus, GCF of Fractions is 1/3060.Finally, GCF of Fractions for 89/68, 69/90, 31/36 is 1/3060.