How to Find GCF of 460/310, 728/120?

GCF of 460/310, 728/120

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 460/310, 728/120 i.e 4/3720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 460/310, 728/120.

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 460/310,728/120?

Given fractions are 460/310,728/120

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 460/310,728/120, numerators are 460,728

Denominators are 310,120

The GCF of 460,728 is 4 .

LCM of 310,120 is 3720.

The greatest common factor of 460/310,728/120 = [GCF of 460,728]/[LCM of 310,120]= 4/3720

Therefore, the GCF of 460/310,728/120 is 4/3720.

Greatest Common Factor of 460,728

To find the highest common factor of 460,728, we have to find the factors of both numbers and list the highest common factor.

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The HCF of 460,728 is 4.

Lets's calculate GCF of 460,728

Greatest Common Factor (GCF) of 460,728 By Common Division

2	460, 728
2	230, 364
	115, 182

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 460,728 By Matching Biggest Common Factor Method

Now, list down the factors of 460

1,2,4,5,10,20,23,46,92,115,230,460

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Greatest Common Factor

We found the factors 460,728 . The biggest common factor number is the GCF number.
So the greatest common factor 460,728 is 4.

Lets's calculate LCM of 310,120

Lowest Common Multiple of 310,120 using Common Division

2	310, 120
5	155, 60
	31, 12

∴ So the LCM of the given numbers is 2 x 5 x 31 x 12 = 3720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3720

Therefore, the GCF of Fractions 460/310,728/120 is 4/3720

Least Common Multiple of 310,120 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 310,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(310,120) = 10

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

GCF(310,120) x common factors =10 x 1 = 10

LCM(310,120) = ( 310 × 120 ) / 10

LCM(310,120) = 37200 / 10

LCM(310,120) = 3720

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FAQs on GCF of Fractions of 460/310, 728/120

1. What is the HCF of 460,728?

The HCF of 460,728 is 4

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 460/310, 728/120?

Answer: GCF of Numerators as per given numbers 460/310, 728/120 is

GCF of Numerators i.e. for 460,728 is 4

LCM of denominators i.e. for 310,120 is 3720.

Thus, GCF of Fractions is 4/3720.Finally, GCF of Fractions for 460/310, 728/120 is 4/3720.