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GCF of 730/18, 154/384

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 730/18, 154/384 i.e 2/1152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/18, 154/384.

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 730/18,154/384?

Given fractions are 730/18,154/384

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 730/18,154/384, numerators are 730,154

Denominators are 18,384

The GCF of 730,154 is 2 .

LCM of 18,384 is 1152.

The greatest common factor of 730/18,154/384 = [GCF of 730,154]/[LCM of 18,384]= 2/1152

Therefore, the GCF of 730/18,154/384 is 2/1152.

Greatest Common Factor of 730,154

To find the highest common factor of 730,154, we have to find the factors of both numbers and list the highest common factor.

The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The HCF of 730,154 is 2.

Lets's calculate GCF of 730,154

Greatest Common Factor (GCF) of 730,154 By Common Division

2 730, 154
365, 77

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 730,154 By Matching Biggest Common Factor Method

Greatest Common Factor of 730,154 By Matching Biggest Common Factor Method

Now, list down the factors of 730

:

1,2,5,10,73,146,365,730

Now, list down the factors of 154

:

1,2,7,11,14,22,77,154

Greatest Common Factor

We found the factors 730,154 . The biggest common factor number is the GCF number.
So the greatest common factor 730,154 is 2.

Lets's calculate LCM of 18,384

Lowest Common Multiple of 18,384 using Common Division

2 18, 384
3 9, 192
3, 64

∴ So the LCM of the given numbers is 2 x 3 x 3 x 64 = 1152

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1152

Therefore, the GCF of Fractions 730/18,154/384 is 2/1152

Least Common Multiple of 18,384 with GCF Formula

Least Common Multiple of 18,384 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 18,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(18,384) = 6

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

GCF(18,384) x common factors =6 x 1 = 6

LCM(18,384) = ( 18 × 384 ) / 6

LCM(18,384) = 6912 / 6

LCM(18,384) = 1152


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FAQs on GCF of Fractions of 730/18, 154/384

1. What is the HCF of 730,154?

The HCF of 730,154 is 2

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 730/18, 154/384?

Answer: GCF of Numerators as per given numbers 730/18, 154/384 is

GCF of Numerators i.e. for 730,154 is 2

LCM of denominators i.e. for 18,384 is 1152.

Thus, GCF of Fractions is 2/1152.Finally, GCF of Fractions for 730/18, 154/384 is 2/1152.