How to Find GCF of 61/40, 40/17, 914/507?

GCF of 61/40, 40/17, 914/507

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 61/40, 40/17, 914/507 i.e 1/344760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/40, 40/17, 914/507.

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 61/40,40/17,914/507?

Given fractions are 61/40,40/17,914/507

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 61/40,40/17,914/507, numerators are 61,40,914

Denominators are 40,17,507

The GCF of 61,40,914 is 1 .

LCM of 40,17,507 is 344760.

The greatest common factor of 61/40,40/17,914/507 = [GCF of 61,40,914]/[LCM of 40,17,507]= 1/344760

Therefore, the GCF of 61/40,40/17,914/507 is 1/344760.

Greatest Common Factor of 61,40,914

To find the highest common factor of 61,40,914, we have to find the factors of both numbers and list the highest common factor.

The factors of 61 are 1, 61

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 914 are 1, 2, 457, 914

The HCF of 61,40,914 is 1.

Lets's calculate GCF of 61,40,914

Greatest Common Factor (GCF) of 61,40,914 By Common Division

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

Greatest Common Factor of 61,40,914 By Matching Biggest Common Factor Method

Now, list down the factors of 61

1,61

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 914

1,2,457,914

Greatest Common Factor

We found the factors 61,40,914 . The biggest common factor number is the GCF number.
So the greatest common factor 61,40,914 is 1.

Lets's calculate LCM of 40,17,507

Lowest Common Multiple of 40,17,507 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 344760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/344760

Therefore, the GCF of Fractions 61/40,40/17,914/507 is 1/344760

Least Common Multiple of 40,17,507 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 40,17,507 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,17,507) = 1

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

GCF(40,17,507) x common factors =1 x 1 = 1

LCM(40,17,507) = ( 40 × 17 × 507 ) / 1

LCM(40,17,507) = 344760 / 1

LCM(40,17,507) = 344760

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FAQs on GCF of Fractions of 61/40, 40/17, 914/507

1. What is the HCF of 61,40,914?

The HCF of 61,40,914 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 61/40, 40/17, 914/507?

Answer: GCF of Numerators as per given numbers 61/40, 40/17, 914/507 is

GCF of Numerators i.e. for 61,40,914 is 1

LCM of denominators i.e. for 40,17,507 is 344760.

Thus, GCF of Fractions is 1/344760.Finally, GCF of Fractions for 61/40, 40/17, 914/507 is 1/344760.