How to Find GCF of 40/266, 53/210, 281/420?

GCF of 40/266, 53/210, 281/420

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 40/266, 53/210, 281/420 i.e 1/7980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/266, 53/210, 281/420.

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 40/266,53/210,281/420?

Given fractions are 40/266,53/210,281/420

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 40/266,53/210,281/420, numerators are 40,53,281

Denominators are 266,210,420

The GCF of 40,53,281 is 1 .

LCM of 266,210,420 is 7980.

The greatest common factor of 40/266,53/210,281/420 = [GCF of 40,53,281]/[LCM of 266,210,420]= 1/7980

Therefore, the GCF of 40/266,53/210,281/420 is 1/7980.

Greatest Common Factor of 40,53,281

To find the highest common factor of 40,53,281, 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 53 are 1, 53

The factors of 281 are 1, 281

The HCF of 40,53,281 is 1.

Lets's calculate GCF of 40,53,281

Greatest Common Factor (GCF) of 40,53,281 By Common Division

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

Greatest Common Factor of 40,53,281 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 53

1,53

Now, list down the factors of 281

1,281

Greatest Common Factor

We found the factors 40,53,281 . The biggest common factor number is the GCF number.
So the greatest common factor 40,53,281 is 1.

Lets's calculate LCM of 266,210,420

Lowest Common Multiple of 266,210,420 using Common Division

2	266, 210, 420
3	133, 105, 210
5	133, 35, 70
7	133, 7, 14
	19, 1, 2

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 19 x 1 x 2 = 7980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7980

Therefore, the GCF of Fractions 40/266,53/210,281/420 is 1/7980

Least Common Multiple of 266,210,420 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 266,210,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(266,210,420) = 14

common factors(in case of two or more numbers have common factors) = 210

GCF(266,210,420) x common factors =14 x 210 = 2940

LCM(266,210,420) = ( 266 × 210 × 420 ) / 2940

LCM(266,210,420) = 23461200 / 2940

LCM(266,210,420) = 7980

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 40/266, 53/210, 281/420

1. What is the HCF of 40,53,281?

The HCF of 40,53,281 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 40/266, 53/210, 281/420?

Answer: GCF of Numerators as per given numbers 40/266, 53/210, 281/420 is

GCF of Numerators i.e. for 40,53,281 is 1

LCM of denominators i.e. for 266,210,420 is 7980.

Thus, GCF of Fractions is 1/7980.Finally, GCF of Fractions for 40/266, 53/210, 281/420 is 1/7980.