How to Find GCF of 21/26, 842/14, 321/671?

GCF of 21/26, 842/14, 321/671

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 21/26, 842/14, 321/671 i.e 1/122122 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/26, 842/14, 321/671.

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 21/26,842/14,321/671?

Given fractions are 21/26,842/14,321/671

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 21/26,842/14,321/671, numerators are 21,842,321

Denominators are 26,14,671

The GCF of 21,842,321 is 1 .

LCM of 26,14,671 is 122122.

The greatest common factor of 21/26,842/14,321/671 = [GCF of 21,842,321]/[LCM of 26,14,671]= 1/122122

Therefore, the GCF of 21/26,842/14,321/671 is 1/122122.

Greatest Common Factor of 21,842,321

To find the highest common factor of 21,842,321, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

The factors of 842 are 1, 2, 421, 842

The factors of 321 are 1, 3, 107, 321

The HCF of 21,842,321 is 1.

Lets's calculate GCF of 21,842,321

Greatest Common Factor (GCF) of 21,842,321 By Common Division

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

Greatest Common Factor of 21,842,321 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 842

1,2,421,842

Now, list down the factors of 321

1,3,107,321

Greatest Common Factor

We found the factors 21,842,321 . The biggest common factor number is the GCF number.
So the greatest common factor 21,842,321 is 1.

Lets's calculate LCM of 26,14,671

Lowest Common Multiple of 26,14,671 using Common Division

2	26, 14, 671
	13, 7, 671

∴ So the LCM of the given numbers is 2 x 13 x 7 x 671 = 122122

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122122

Therefore, the GCF of Fractions 21/26,842/14,321/671 is 1/122122

Least Common Multiple of 26,14,671 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 26,14,671 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,14,671) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(26,14,671) x common factors =1 x 2 = 2

LCM(26,14,671) = ( 26 × 14 × 671 ) / 2

LCM(26,14,671) = 244244 / 2

LCM(26,14,671) = 122122

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FAQs on GCF of Fractions of 21/26, 842/14, 321/671

1. What is the HCF of 21,842,321?

The HCF of 21,842,321 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 21/26, 842/14, 321/671?

Answer: GCF of Numerators as per given numbers 21/26, 842/14, 321/671 is

GCF of Numerators i.e. for 21,842,321 is 1

LCM of denominators i.e. for 26,14,671 is 122122.

Thus, GCF of Fractions is 1/122122.Finally, GCF of Fractions for 21/26, 842/14, 321/671 is 1/122122.