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GCF of 459/28, 414/3324

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 459/28, 414/3324 i.e 9/23268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/28, 414/3324.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 459/28,414/3324?

Given fractions are 459/28,414/3324

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 459/28,414/3324, numerators are 459,414

Denominators are 28,3324

The GCF of 459,414 is 9 .

LCM of 28,3324 is 23268.

The greatest common factor of 459/28,414/3324 = [GCF of 459,414]/[LCM of 28,3324]= 9/23268

Therefore, the GCF of 459/28,414/3324 is 9/23268.

Greatest Common Factor of 459,414

To find the highest common factor of 459,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 459,414 is 9.

Lets's calculate GCF of 459,414

Greatest Common Factor (GCF) of 459,414 By Common Division

3 459, 414
3 153, 138
51, 46

∴ So the GCF of the given numbers is 3 x 3 = 9

Greatest Common Factor of 459,414 By Matching Biggest Common Factor Method

Greatest Common Factor of 459,414 By Matching Biggest Common Factor Method

Now, list down the factors of 459

:

1,3,9,17,27,51,153,459

Now, list down the factors of 414

:

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 459,414 . The biggest common factor number is the GCF number.
So the greatest common factor 459,414 is 9.

Lets's calculate LCM of 28,3324

Lowest Common Multiple of 28,3324 using Common Division

2 28, 3324
2 14, 1662
7, 831

∴ So the LCM of the given numbers is 2 x 2 x 7 x 831 = 23268

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/23268

Therefore, the GCF of Fractions 459/28,414/3324 is 9/23268

Least Common Multiple of 28,3324 with GCF Formula

Least Common Multiple of 28,3324 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 28,3324 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,3324) = 4

common factors(in case of two or more numbers have common factors) = 1

GCF(28,3324) x common factors =4 x 1 = 4

LCM(28,3324) = ( 28 × 3324 ) / 4

LCM(28,3324) = 93072 / 4

LCM(28,3324) = 23268


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FAQs on GCF of Fractions of 459/28, 414/3324

1. What is the HCF of 459,414?

The HCF of 459,414 is 9

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 459/28, 414/3324?

Answer: GCF of Numerators as per given numbers 459/28, 414/3324 is

GCF of Numerators i.e. for 459,414 is 9

LCM of denominators i.e. for 28,3324 is 23268.

Thus, GCF of Fractions is 9/23268.Finally, GCF of Fractions for 459/28, 414/3324 is 9/23268.