How to Find GCF of 14/68, 21/150, 553/306?

GCF of 14/68, 21/150, 553/306

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 14/68, 21/150, 553/306 i.e 7/15300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/68, 21/150, 553/306.

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 14/68,21/150,553/306?

Given fractions are 14/68,21/150,553/306

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 14/68,21/150,553/306, numerators are 14,21,553

Denominators are 68,150,306

The GCF of 14,21,553 is 7 .

LCM of 68,150,306 is 15300.

The greatest common factor of 14/68,21/150,553/306 = [GCF of 14,21,553]/[LCM of 68,150,306]= 7/15300

Therefore, the GCF of 14/68,21/150,553/306 is 7/15300.

Greatest Common Factor of 14,21,553

To find the highest common factor of 14,21,553, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

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

The factors of 553 are 1, 7, 79, 553

The HCF of 14,21,553 is 7.

Lets's calculate GCF of 14,21,553

Greatest Common Factor (GCF) of 14,21,553 By Common Division

7	14, 21, 553
	2, 3, 79

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 14,21,553 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 553

1,7,79,553

Greatest Common Factor

We found the factors 14,21,553 . The biggest common factor number is the GCF number.
So the greatest common factor 14,21,553 is 7.

Lets's calculate LCM of 68,150,306

Lowest Common Multiple of 68,150,306 using Common Division

2	68, 150, 306
3	34, 75, 153
17	34, 25, 51
	2, 25, 3

∴ So the LCM of the given numbers is 2 x 3 x 17 x 2 x 25 x 3 = 15300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/15300

Therefore, the GCF of Fractions 14/68,21/150,553/306 is 7/15300

Least Common Multiple of 68,150,306 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 68,150,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,150,306) = 2

common factors(in case of two or more numbers have common factors) = 102

GCF(68,150,306) x common factors =2 x 102 = 204

LCM(68,150,306) = ( 68 × 150 × 306 ) / 204

LCM(68,150,306) = 3121200 / 204

LCM(68,150,306) = 15300

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/68, 21/150, 553/306

1. What is the HCF of 14,21,553?

The HCF of 14,21,553 is 7

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 14/68, 21/150, 553/306?

Answer: GCF of Numerators as per given numbers 14/68, 21/150, 553/306 is

GCF of Numerators i.e. for 14,21,553 is 7

LCM of denominators i.e. for 68,150,306 is 15300.

Thus, GCF of Fractions is 7/15300.Finally, GCF of Fractions for 14/68, 21/150, 553/306 is 7/15300.