How to Find GCF of 449/64, 342/960?

GCF of 449/64, 342/960

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 449/64, 342/960 i.e 1/960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 449/64, 342/960.

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 449/64,342/960?

Given fractions are 449/64,342/960

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 449/64,342/960, numerators are 449,342

Denominators are 64,960

The GCF of 449,342 is 1 .

LCM of 64,960 is 960.

The greatest common factor of 449/64,342/960 = [GCF of 449,342]/[LCM of 64,960]= 1/960

Therefore, the GCF of 449/64,342/960 is 1/960.

Greatest Common Factor of 449,342

To find the highest common factor of 449,342, we have to find the factors of both numbers and list the highest common factor.

The factors of 449 are 1, 449

The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342

The HCF of 449,342 is 1.

Lets's calculate GCF of 449,342

Greatest Common Factor (GCF) of 449,342 By Common Division

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

Greatest Common Factor of 449,342 By Matching Biggest Common Factor Method

Now, list down the factors of 449

1,449

Now, list down the factors of 342

1,2,3,6,9,18,19,38,57,114,171,342

Greatest Common Factor

We found the factors 449,342 . The biggest common factor number is the GCF number.
So the greatest common factor 449,342 is 1.

Lets's calculate LCM of 64,960

Lowest Common Multiple of 64,960 using Common Division

2	64, 960
2	32, 480
2	16, 240
2	8, 120
2	4, 60
2	2, 30
	1, 15

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 1 x 15 = 960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/960

Therefore, the GCF of Fractions 449/64,342/960 is 1/960

Least Common Multiple of 64,960 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 64,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,960) = 64

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

GCF(64,960) x common factors =64 x 1 = 64

LCM(64,960) = ( 64 × 960 ) / 64

LCM(64,960) = 61440 / 64

LCM(64,960) = 960

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FAQs on GCF of Fractions of 449/64, 342/960

1. What is the HCF of 449,342?

The HCF of 449,342 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 449/64, 342/960?

Answer: GCF of Numerators as per given numbers 449/64, 342/960 is

GCF of Numerators i.e. for 449,342 is 1

LCM of denominators i.e. for 64,960 is 960.

Thus, GCF of Fractions is 1/960.Finally, GCF of Fractions for 449/64, 342/960 is 1/960.