How to Find GCF of 21/10, 523/78, 105/446?

GCF of 21/10, 523/78, 105/446

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 21/10, 523/78, 105/446 i.e 1/86970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/10, 523/78, 105/446.

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 21/10,523/78,105/446?

Given fractions are 21/10,523/78,105/446

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 21/10,523/78,105/446, numerators are 21,523,105

Denominators are 10,78,446

The GCF of 21,523,105 is 1 .

LCM of 10,78,446 is 86970.

The greatest common factor of 21/10,523/78,105/446 = [GCF of 21,523,105]/[LCM of 10,78,446]= 1/86970

Therefore, the GCF of 21/10,523/78,105/446 is 1/86970.

Greatest Common Factor of 21,523,105

To find the highest common factor of 21,523,105, 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 523 are 1, 523

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The HCF of 21,523,105 is 1.

Lets's calculate GCF of 21,523,105

Greatest Common Factor (GCF) of 21,523,105 By Common Division

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

Greatest Common Factor of 21,523,105 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 523

1,523

Now, list down the factors of 105

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 21,523,105 . The biggest common factor number is the GCF number.
So the greatest common factor 21,523,105 is 1.

Lets's calculate LCM of 10,78,446

Lowest Common Multiple of 10,78,446 using Common Division

2	10, 78, 446
	5, 39, 223

∴ So the LCM of the given numbers is 2 x 5 x 39 x 223 = 86970

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/86970

Therefore, the GCF of Fractions 21/10,523/78,105/446 is 1/86970

Least Common Multiple of 10,78,446 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 10,78,446 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(10,78,446) = 2

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

GCF(10,78,446) x common factors =2 x 2 = 4

LCM(10,78,446) = ( 10 × 78 × 446 ) / 4

LCM(10,78,446) = 347880 / 4

LCM(10,78,446) = 86970

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FAQs on GCF of Fractions of 21/10, 523/78, 105/446

1. What is the HCF of 21,523,105?

The HCF of 21,523,105 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 21/10, 523/78, 105/446?

Answer: GCF of Numerators as per given numbers 21/10, 523/78, 105/446 is

GCF of Numerators i.e. for 21,523,105 is 1

LCM of denominators i.e. for 10,78,446 is 86970.

Thus, GCF of Fractions is 1/86970.Finally, GCF of Fractions for 21/10, 523/78, 105/446 is 1/86970.