How to Find GCF of 410/68, 601/20, 319/21?

GCF of 410/68, 601/20, 319/21

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 410/68, 601/20, 319/21 i.e 1/7140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/68, 601/20, 319/21.

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 410/68,601/20,319/21?

Given fractions are 410/68,601/20,319/21

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 410/68,601/20,319/21, numerators are 410,601,319

Denominators are 68,20,21

The GCF of 410,601,319 is 1 .

LCM of 68,20,21 is 7140.

The greatest common factor of 410/68,601/20,319/21 = [GCF of 410,601,319]/[LCM of 68,20,21]= 1/7140

Therefore, the GCF of 410/68,601/20,319/21 is 1/7140.

Greatest Common Factor of 410,601,319

To find the highest common factor of 410,601,319, we have to find the factors of both numbers and list the highest common factor.

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410

The factors of 601 are 1, 601

The factors of 319 are 1, 11, 29, 319

The HCF of 410,601,319 is 1.

Lets's calculate GCF of 410,601,319

Greatest Common Factor (GCF) of 410,601,319 By Common Division

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

Greatest Common Factor of 410,601,319 By Matching Biggest Common Factor Method

Now, list down the factors of 410

1,2,5,10,41,82,205,410

Now, list down the factors of 601

1,601

Now, list down the factors of 319

1,11,29,319

Greatest Common Factor

We found the factors 410,601,319 . The biggest common factor number is the GCF number.
So the greatest common factor 410,601,319 is 1.

Lets's calculate LCM of 68,20,21

Lowest Common Multiple of 68,20,21 using Common Division

2	68, 20, 21
2	34, 10, 21
	17, 5, 21

∴ So the LCM of the given numbers is 2 x 2 x 17 x 5 x 21 = 7140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7140

Therefore, the GCF of Fractions 410/68,601/20,319/21 is 1/7140

Least Common Multiple of 68,20,21 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 68,20,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,20,21) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(68,20,21) x common factors =1 x 4 = 4

LCM(68,20,21) = ( 68 × 20 × 21 ) / 4

LCM(68,20,21) = 28560 / 4

LCM(68,20,21) = 7140

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FAQs on GCF of Fractions of 410/68, 601/20, 319/21

1. What is the HCF of 410,601,319?

The HCF of 410,601,319 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 410/68, 601/20, 319/21?

Answer: GCF of Numerators as per given numbers 410/68, 601/20, 319/21 is

GCF of Numerators i.e. for 410,601,319 is 1

LCM of denominators i.e. for 68,20,21 is 7140.

Thus, GCF of Fractions is 1/7140.Finally, GCF of Fractions for 410/68, 601/20, 319/21 is 1/7140.