How to Find GCF of 40/56, 225/67, 682/146?

GCF of 40/56, 225/67, 682/146

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 40/56, 225/67, 682/146 i.e 1/273896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/56, 225/67, 682/146.

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 40/56,225/67,682/146?

Given fractions are 40/56,225/67,682/146

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 40/56,225/67,682/146, numerators are 40,225,682

Denominators are 56,67,146

The GCF of 40,225,682 is 1 .

LCM of 56,67,146 is 273896.

The greatest common factor of 40/56,225/67,682/146 = [GCF of 40,225,682]/[LCM of 56,67,146]= 1/273896

Therefore, the GCF of 40/56,225/67,682/146 is 1/273896.

Greatest Common Factor of 40,225,682

To find the highest common factor of 40,225,682, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The HCF of 40,225,682 is 1.

Lets's calculate GCF of 40,225,682

Greatest Common Factor (GCF) of 40,225,682 By Common Division

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

Greatest Common Factor of 40,225,682 By Matching Biggest Common Factor Method

Now, list down the factors of 40

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

Now, list down the factors of 225

1,3,5,9,15,25,45,75,225

Now, list down the factors of 682

1,2,11,22,31,62,341,682

Greatest Common Factor

We found the factors 40,225,682 . The biggest common factor number is the GCF number.
So the greatest common factor 40,225,682 is 1.

Lets's calculate LCM of 56,67,146

Lowest Common Multiple of 56,67,146 using Common Division

2	56, 67, 146
	28, 67, 73

∴ So the LCM of the given numbers is 2 x 28 x 67 x 73 = 273896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/273896

Therefore, the GCF of Fractions 40/56,225/67,682/146 is 1/273896

Least Common Multiple of 56,67,146 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 56,67,146 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(56,67,146) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(56,67,146) x common factors =1 x 2 = 2

LCM(56,67,146) = ( 56 × 67 × 146 ) / 2

LCM(56,67,146) = 547792 / 2

LCM(56,67,146) = 273896

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 40/56, 225/67, 682/146

1. What is the HCF of 40,225,682?

The HCF of 40,225,682 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 40/56, 225/67, 682/146?

Answer: GCF of Numerators as per given numbers 40/56, 225/67, 682/146 is

GCF of Numerators i.e. for 40,225,682 is 1

LCM of denominators i.e. for 56,67,146 is 273896.

Thus, GCF of Fractions is 1/273896.Finally, GCF of Fractions for 40/56, 225/67, 682/146 is 1/273896.