How to Find GCF of 68/76, 65/72, 421/21?

GCF of 68/76, 65/72, 421/21

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 68/76, 65/72, 421/21 i.e 1/9576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/76, 65/72, 421/21.

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 68/76,65/72,421/21?

Given fractions are 68/76,65/72,421/21

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 68/76,65/72,421/21, numerators are 68,65,421

Denominators are 76,72,21

The GCF of 68,65,421 is 1 .

LCM of 76,72,21 is 9576.

The greatest common factor of 68/76,65/72,421/21 = [GCF of 68,65,421]/[LCM of 76,72,21]= 1/9576

Therefore, the GCF of 68/76,65/72,421/21 is 1/9576.

Greatest Common Factor of 68,65,421

To find the highest common factor of 68,65,421, we have to find the factors of both numbers and list the highest common factor.

The factors of 68 are 1, 2, 4, 17, 34, 68

The factors of 65 are 1, 5, 13, 65

The factors of 421 are 1, 421

The HCF of 68,65,421 is 1.

Lets's calculate GCF of 68,65,421

Greatest Common Factor (GCF) of 68,65,421 By Common Division

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

Greatest Common Factor of 68,65,421 By Matching Biggest Common Factor Method

Now, list down the factors of 68

1,2,4,17,34,68

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 421

1,421

Greatest Common Factor

We found the factors 68,65,421 . The biggest common factor number is the GCF number.
So the greatest common factor 68,65,421 is 1.

Lets's calculate LCM of 76,72,21

Lowest Common Multiple of 76,72,21 using Common Division

2	76, 72, 21
2	38, 36, 21
3	19, 18, 21
	19, 6, 7

∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 6 x 7 = 9576

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9576

Therefore, the GCF of Fractions 68/76,65/72,421/21 is 1/9576

Least Common Multiple of 76,72,21 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 76,72,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,72,21) = 1

common factors(in case of two or more numbers have common factors) = 12

GCF(76,72,21) x common factors =1 x 12 = 12

LCM(76,72,21) = ( 76 × 72 × 21 ) / 12

LCM(76,72,21) = 114912 / 12

LCM(76,72,21) = 9576

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FAQs on GCF of Fractions of 68/76, 65/72, 421/21

1. What is the HCF of 68,65,421?

The HCF of 68,65,421 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 68/76, 65/72, 421/21?

Answer: GCF of Numerators as per given numbers 68/76, 65/72, 421/21 is

GCF of Numerators i.e. for 68,65,421 is 1

LCM of denominators i.e. for 76,72,21 is 9576.

Thus, GCF of Fractions is 1/9576.Finally, GCF of Fractions for 68/76, 65/72, 421/21 is 1/9576.