How to Find GCF of 65/31, 37/76, 918/29?

GCF of 65/31, 37/76, 918/29

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 65/31, 37/76, 918/29 i.e 1/68324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/31, 37/76, 918/29.

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 65/31,37/76,918/29?

Given fractions are 65/31,37/76,918/29

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 65/31,37/76,918/29, numerators are 65,37,918

Denominators are 31,76,29

The GCF of 65,37,918 is 1 .

LCM of 31,76,29 is 68324.

The greatest common factor of 65/31,37/76,918/29 = [GCF of 65,37,918]/[LCM of 31,76,29]= 1/68324

Therefore, the GCF of 65/31,37/76,918/29 is 1/68324.

Greatest Common Factor of 65,37,918

To find the highest common factor of 65,37,918, we have to find the factors of both numbers and list the highest common factor.

The factors of 65 are 1, 5, 13, 65

The factors of 37 are 1, 37

The factors of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918

The HCF of 65,37,918 is 1.

Lets's calculate GCF of 65,37,918

Greatest Common Factor (GCF) of 65,37,918 By Common Division

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

Greatest Common Factor of 65,37,918 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 37

1,37

Now, list down the factors of 918

1,2,3,6,9,17,18,27,34,51,54,102,153,306,459,918

Greatest Common Factor

We found the factors 65,37,918 . The biggest common factor number is the GCF number.
So the greatest common factor 65,37,918 is 1.

Lets's calculate LCM of 31,76,29

Lowest Common Multiple of 31,76,29 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 68324

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68324

Therefore, the GCF of Fractions 65/31,37/76,918/29 is 1/68324

Least Common Multiple of 31,76,29 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 31,76,29 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,76,29) = 1

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

GCF(31,76,29) x common factors =1 x 1 = 1

LCM(31,76,29) = ( 31 × 76 × 29 ) / 1

LCM(31,76,29) = 68324 / 1

LCM(31,76,29) = 68324

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 65/31, 37/76, 918/29

1. What is the HCF of 65,37,918?

The HCF of 65,37,918 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 65/31, 37/76, 918/29?

Answer: GCF of Numerators as per given numbers 65/31, 37/76, 918/29 is

GCF of Numerators i.e. for 65,37,918 is 1

LCM of denominators i.e. for 31,76,29 is 68324.

Thus, GCF of Fractions is 1/68324.Finally, GCF of Fractions for 65/31, 37/76, 918/29 is 1/68324.