How to Find GCF of 65/78, 36/80, 499/280?

GCF of 65/78, 36/80, 499/280

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 65/78, 36/80, 499/280 i.e 1/21840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/78, 36/80, 499/280.

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 65/78,36/80,499/280?

Given fractions are 65/78,36/80,499/280

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 65/78,36/80,499/280, numerators are 65,36,499

Denominators are 78,80,280

The GCF of 65,36,499 is 1 .

LCM of 78,80,280 is 21840.

The greatest common factor of 65/78,36/80,499/280 = [GCF of 65,36,499]/[LCM of 78,80,280]= 1/21840

Therefore, the GCF of 65/78,36/80,499/280 is 1/21840.

Greatest Common Factor of 65,36,499

To find the highest common factor of 65,36,499, 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 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 499 are 1, 499

The HCF of 65,36,499 is 1.

Lets's calculate GCF of 65,36,499

Greatest Common Factor (GCF) of 65,36,499 By Common Division

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

Greatest Common Factor of 65,36,499 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 36

1,2,3,4,6,9,12,18,36

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 65,36,499 . The biggest common factor number is the GCF number.
So the greatest common factor 65,36,499 is 1.

Lets's calculate LCM of 78,80,280

Lowest Common Multiple of 78,80,280 using Common Division

2	78, 80, 280
2	39, 40, 140
2	39, 20, 70
5	39, 10, 35
	39, 2, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 39 x 2 x 7 = 21840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21840

Therefore, the GCF of Fractions 65/78,36/80,499/280 is 1/21840

Least Common Multiple of 78,80,280 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 78,80,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,80,280) = 2

common factors(in case of two or more numbers have common factors) = 40

GCF(78,80,280) x common factors =2 x 40 = 80

LCM(78,80,280) = ( 78 × 80 × 280 ) / 80

LCM(78,80,280) = 1747200 / 80

LCM(78,80,280) = 21840

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 65/78, 36/80, 499/280

1. What is the HCF of 65,36,499?

The HCF of 65,36,499 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 65/78, 36/80, 499/280?

Answer: GCF of Numerators as per given numbers 65/78, 36/80, 499/280 is

GCF of Numerators i.e. for 65,36,499 is 1

LCM of denominators i.e. for 78,80,280 is 21840.

Thus, GCF of Fractions is 1/21840.Finally, GCF of Fractions for 65/78, 36/80, 499/280 is 1/21840.