How to Find GCF of 34/304, 449/196, 142/628?

GCF of 34/304, 449/196, 142/628

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 34/304, 449/196, 142/628 i.e 1/2338672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/304, 449/196, 142/628.

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 34/304,449/196,142/628?

Given fractions are 34/304,449/196,142/628

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 34/304,449/196,142/628, numerators are 34,449,142

Denominators are 304,196,628

The GCF of 34,449,142 is 1 .

LCM of 304,196,628 is 2338672.

The greatest common factor of 34/304,449/196,142/628 = [GCF of 34,449,142]/[LCM of 304,196,628]= 1/2338672

Therefore, the GCF of 34/304,449/196,142/628 is 1/2338672.

Greatest Common Factor of 34,449,142

To find the highest common factor of 34,449,142, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 449 are 1, 449

The factors of 142 are 1, 2, 71, 142

The HCF of 34,449,142 is 1.

Lets's calculate GCF of 34,449,142

Greatest Common Factor (GCF) of 34,449,142 By Common Division

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

Greatest Common Factor of 34,449,142 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 449

1,449

Now, list down the factors of 142

1,2,71,142

Greatest Common Factor

We found the factors 34,449,142 . The biggest common factor number is the GCF number.
So the greatest common factor 34,449,142 is 1.

Lets's calculate LCM of 304,196,628

Lowest Common Multiple of 304,196,628 using Common Division

2	304, 196, 628
2	152, 98, 314
	76, 49, 157

∴ So the LCM of the given numbers is 2 x 2 x 76 x 49 x 157 = 2338672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2338672

Therefore, the GCF of Fractions 34/304,449/196,142/628 is 1/2338672

Least Common Multiple of 304,196,628 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 304,196,628 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(304,196,628) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(304,196,628) x common factors =4 x 4 = 16

LCM(304,196,628) = ( 304 × 196 × 628 ) / 16

LCM(304,196,628) = 37418752 / 16

LCM(304,196,628) = 2338672

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FAQs on GCF of Fractions of 34/304, 449/196, 142/628

1. What is the HCF of 34,449,142?

The HCF of 34,449,142 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 34/304, 449/196, 142/628?

Answer: GCF of Numerators as per given numbers 34/304, 449/196, 142/628 is

GCF of Numerators i.e. for 34,449,142 is 1

LCM of denominators i.e. for 304,196,628 is 2338672.

Thus, GCF of Fractions is 1/2338672.Finally, GCF of Fractions for 34/304, 449/196, 142/628 is 1/2338672.