How to Find GCF of 326/74, 582/77, 429/24?

GCF of 326/74, 582/77, 429/24

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 326/74, 582/77, 429/24 i.e 1/68376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 326/74, 582/77, 429/24.

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 326/74,582/77,429/24?

Given fractions are 326/74,582/77,429/24

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 326/74,582/77,429/24, numerators are 326,582,429

Denominators are 74,77,24

The GCF of 326,582,429 is 1 .

LCM of 74,77,24 is 68376.

The greatest common factor of 326/74,582/77,429/24 = [GCF of 326,582,429]/[LCM of 74,77,24]= 1/68376

Therefore, the GCF of 326/74,582/77,429/24 is 1/68376.

Greatest Common Factor of 326,582,429

To find the highest common factor of 326,582,429, we have to find the factors of both numbers and list the highest common factor.

The factors of 326 are 1, 2, 163, 326

The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582

The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429

The HCF of 326,582,429 is 1.

Lets's calculate GCF of 326,582,429

Greatest Common Factor (GCF) of 326,582,429 By Common Division

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

Greatest Common Factor of 326,582,429 By Matching Biggest Common Factor Method

Now, list down the factors of 326

1,2,163,326

Now, list down the factors of 582

1,2,3,6,97,194,291,582

Now, list down the factors of 429

1,3,11,13,33,39,143,429

Greatest Common Factor

We found the factors 326,582,429 . The biggest common factor number is the GCF number.
So the greatest common factor 326,582,429 is 1.

Lets's calculate LCM of 74,77,24

Lowest Common Multiple of 74,77,24 using Common Division

2	74, 77, 24
	37, 77, 12

∴ So the LCM of the given numbers is 2 x 37 x 77 x 12 = 68376

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68376

Therefore, the GCF of Fractions 326/74,582/77,429/24 is 1/68376

Least Common Multiple of 74,77,24 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 74,77,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,77,24) = 1

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

GCF(74,77,24) x common factors =1 x 2 = 2

LCM(74,77,24) = ( 74 × 77 × 24 ) / 2

LCM(74,77,24) = 136752 / 2

LCM(74,77,24) = 68376

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FAQs on GCF of Fractions of 326/74, 582/77, 429/24

1. What is the HCF of 326,582,429?

The HCF of 326,582,429 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 326/74, 582/77, 429/24?

Answer: GCF of Numerators as per given numbers 326/74, 582/77, 429/24 is

GCF of Numerators i.e. for 326,582,429 is 1

LCM of denominators i.e. for 74,77,24 is 68376.

Thus, GCF of Fractions is 1/68376.Finally, GCF of Fractions for 326/74, 582/77, 429/24 is 1/68376.