How to Find GCF of 21/35, 19/84, 257/716?

GCF of 21/35, 19/84, 257/716

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 21/35, 19/84, 257/716 i.e 1/75180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/35, 19/84, 257/716.

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 21/35,19/84,257/716?

Given fractions are 21/35,19/84,257/716

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 21/35,19/84,257/716, numerators are 21,19,257

Denominators are 35,84,716

The GCF of 21,19,257 is 1 .

LCM of 35,84,716 is 75180.

The greatest common factor of 21/35,19/84,257/716 = [GCF of 21,19,257]/[LCM of 35,84,716]= 1/75180

Therefore, the GCF of 21/35,19/84,257/716 is 1/75180.

Greatest Common Factor of 21,19,257

To find the highest common factor of 21,19,257, 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 19 are 1, 19

The factors of 257 are 1, 257

The HCF of 21,19,257 is 1.

Lets's calculate GCF of 21,19,257

Greatest Common Factor (GCF) of 21,19,257 By Common Division

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

Greatest Common Factor of 21,19,257 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 19

1,19

Now, list down the factors of 257

1,257

Greatest Common Factor

We found the factors 21,19,257 . The biggest common factor number is the GCF number.
So the greatest common factor 21,19,257 is 1.

Lets's calculate LCM of 35,84,716

Lowest Common Multiple of 35,84,716 using Common Division

2	35, 84, 716
2	35, 42, 358
7	35, 21, 179
	5, 3, 179

∴ So the LCM of the given numbers is 2 x 2 x 7 x 5 x 3 x 179 = 75180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75180

Therefore, the GCF of Fractions 21/35,19/84,257/716 is 1/75180

Least Common Multiple of 35,84,716 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 35,84,716 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(35,84,716) = 1

common factors(in case of two or more numbers have common factors) = 28

GCF(35,84,716) x common factors =1 x 28 = 28

LCM(35,84,716) = ( 35 × 84 × 716 ) / 28

LCM(35,84,716) = 2105040 / 28

LCM(35,84,716) = 75180

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FAQs on GCF of Fractions of 21/35, 19/84, 257/716

1. What is the HCF of 21,19,257?

The HCF of 21,19,257 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 21/35, 19/84, 257/716?

Answer: GCF of Numerators as per given numbers 21/35, 19/84, 257/716 is

GCF of Numerators i.e. for 21,19,257 is 1

LCM of denominators i.e. for 35,84,716 is 75180.

Thus, GCF of Fractions is 1/75180.Finally, GCF of Fractions for 21/35, 19/84, 257/716 is 1/75180.