How to Find GCF of 14/61, 45/10, 811/105?

GCF of 14/61, 45/10, 811/105

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 14/61, 45/10, 811/105 i.e 1/12810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/61, 45/10, 811/105.

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 14/61,45/10,811/105?

Given fractions are 14/61,45/10,811/105

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 14/61,45/10,811/105, numerators are 14,45,811

Denominators are 61,10,105

The GCF of 14,45,811 is 1 .

LCM of 61,10,105 is 12810.

The greatest common factor of 14/61,45/10,811/105 = [GCF of 14,45,811]/[LCM of 61,10,105]= 1/12810

Therefore, the GCF of 14/61,45/10,811/105 is 1/12810.

Greatest Common Factor of 14,45,811

To find the highest common factor of 14,45,811, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 45 are 1, 3, 5, 9, 15, 45

The factors of 811 are 1, 811

The HCF of 14,45,811 is 1.

Lets's calculate GCF of 14,45,811

Greatest Common Factor (GCF) of 14,45,811 By Common Division

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

Greatest Common Factor of 14,45,811 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 45

1,3,5,9,15,45

Now, list down the factors of 811

1,811

Greatest Common Factor

We found the factors 14,45,811 . The biggest common factor number is the GCF number.
So the greatest common factor 14,45,811 is 1.

Lets's calculate LCM of 61,10,105

Lowest Common Multiple of 61,10,105 using Common Division

5	61, 10, 105
	61, 2, 21

∴ So the LCM of the given numbers is 5 x 61 x 2 x 21 = 12810

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12810

Therefore, the GCF of Fractions 14/61,45/10,811/105 is 1/12810

Least Common Multiple of 61,10,105 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 61,10,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(61,10,105) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(61,10,105) x common factors =1 x 5 = 5

LCM(61,10,105) = ( 61 × 10 × 105 ) / 5

LCM(61,10,105) = 64050 / 5

LCM(61,10,105) = 12810

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FAQs on GCF of Fractions of 14/61, 45/10, 811/105

1. What is the HCF of 14,45,811?

The HCF of 14,45,811 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 14/61, 45/10, 811/105?

Answer: GCF of Numerators as per given numbers 14/61, 45/10, 811/105 is

GCF of Numerators i.e. for 14,45,811 is 1

LCM of denominators i.e. for 61,10,105 is 12810.

Thus, GCF of Fractions is 1/12810.Finally, GCF of Fractions for 14/61, 45/10, 811/105 is 1/12810.