How to Find GCF of 65/400, 22/952, 506/586?

GCF of 65/400, 22/952, 506/586

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 65/400, 22/952, 506/586 i.e 1/13946800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/400, 22/952, 506/586.

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 65/400,22/952,506/586?

Given fractions are 65/400,22/952,506/586

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 65/400,22/952,506/586, numerators are 65,22,506

Denominators are 400,952,586

The GCF of 65,22,506 is 1 .

LCM of 400,952,586 is 13946800.

The greatest common factor of 65/400,22/952,506/586 = [GCF of 65,22,506]/[LCM of 400,952,586]= 1/13946800

Therefore, the GCF of 65/400,22/952,506/586 is 1/13946800.

Greatest Common Factor of 65,22,506

To find the highest common factor of 65,22,506, 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 22 are 1, 2, 11, 22

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 65,22,506 is 1.

Lets's calculate GCF of 65,22,506

Greatest Common Factor (GCF) of 65,22,506 By Common Division

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

Greatest Common Factor of 65,22,506 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 22

1,2,11,22

Now, list down the factors of 506

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 65,22,506 . The biggest common factor number is the GCF number.
So the greatest common factor 65,22,506 is 1.

Lets's calculate LCM of 400,952,586

Lowest Common Multiple of 400,952,586 using Common Division

2	400, 952, 586
2	200, 476, 293
2	100, 238, 293
	50, 119, 293

∴ So the LCM of the given numbers is 2 x 2 x 2 x 50 x 119 x 293 = 13946800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13946800

Therefore, the GCF of Fractions 65/400,22/952,506/586 is 1/13946800

Least Common Multiple of 400,952,586 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 400,952,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,952,586) = 2

common factors(in case of two or more numbers have common factors) = 8

GCF(400,952,586) x common factors =2 x 8 = 16

LCM(400,952,586) = ( 400 × 952 × 586 ) / 16

LCM(400,952,586) = 223148800 / 16

LCM(400,952,586) = 13946800

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 65/400, 22/952, 506/586

1. What is the HCF of 65,22,506?

The HCF of 65,22,506 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 65/400, 22/952, 506/586?

Answer: GCF of Numerators as per given numbers 65/400, 22/952, 506/586 is

GCF of Numerators i.e. for 65,22,506 is 1

LCM of denominators i.e. for 400,952,586 is 13946800.

Thus, GCF of Fractions is 1/13946800.Finally, GCF of Fractions for 65/400, 22/952, 506/586 is 1/13946800.