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GCF of 204/312, 730/167

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 204/312, 730/167 i.e 2/52104 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/312, 730/167.

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 204/312,730/167?

Given fractions are 204/312,730/167

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 204/312,730/167, numerators are 204,730

Denominators are 312,167

The GCF of 204,730 is 2 .

LCM of 312,167 is 52104.

The greatest common factor of 204/312,730/167 = [GCF of 204,730]/[LCM of 312,167]= 2/52104

Therefore, the GCF of 204/312,730/167 is 2/52104.

Greatest Common Factor of 204,730

To find the highest common factor of 204,730, we have to find the factors of both numbers and list the highest common factor.

The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

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

The HCF of 204,730 is 2.

Lets's calculate GCF of 204,730

Greatest Common Factor (GCF) of 204,730 By Common Division

2 204, 730
102, 365

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

Greatest Common Factor of 204,730 By Matching Biggest Common Factor Method

Greatest Common Factor of 204,730 By Matching Biggest Common Factor Method

Now, list down the factors of 204

:

1,2,3,4,6,12,17,34,51,68,102,204

Now, list down the factors of 730

:

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

Greatest Common Factor

We found the factors 204,730 . The biggest common factor number is the GCF number.
So the greatest common factor 204,730 is 2.

Lets's calculate LCM of 312,167

Lowest Common Multiple of 312,167 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 52104

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/52104

Therefore, the GCF of Fractions 204/312,730/167 is 2/52104

Least Common Multiple of 312,167 with GCF Formula

Least Common Multiple of 312,167 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 312,167 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,167) = 1

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

GCF(312,167) x common factors =1 x 1 = 1

LCM(312,167) = ( 312 × 167 ) / 1

LCM(312,167) = 52104 / 1

LCM(312,167) = 52104


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FAQs on GCF of Fractions of 204/312, 730/167

1. What is the HCF of 204,730?

The HCF of 204,730 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 204/312, 730/167?

Answer: GCF of Numerators as per given numbers 204/312, 730/167 is

GCF of Numerators i.e. for 204,730 is 2

LCM of denominators i.e. for 312,167 is 52104.

Thus, GCF of Fractions is 2/52104.Finally, GCF of Fractions for 204/312, 730/167 is 2/52104.