How to Find GCF of 474/360, 5440/164?

GCF of 474/360, 5440/164

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 474/360, 5440/164 i.e 2/14760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 474/360, 5440/164.

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 474/360,5440/164?

Given fractions are 474/360,5440/164

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 474/360,5440/164, numerators are 474,5440

Denominators are 360,164

The GCF of 474,5440 is 2 .

LCM of 360,164 is 14760.

The greatest common factor of 474/360,5440/164 = [GCF of 474,5440]/[LCM of 360,164]= 2/14760

Therefore, the GCF of 474/360,5440/164 is 2/14760.

Greatest Common Factor of 474,5440

To find the highest common factor of 474,5440, we have to find the factors of both numbers and list the highest common factor.

The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474

The factors of 5440 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 136, 160, 170, 272, 320, 340, 544, 680, 1088, 1360, 2720, 5440

The HCF of 474,5440 is 2.

Lets's calculate GCF of 474,5440

Greatest Common Factor (GCF) of 474,5440 By Common Division

2	474, 5440
	237, 2720

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

Greatest Common Factor of 474,5440 By Matching Biggest Common Factor Method

Now, list down the factors of 474

1,2,3,6,79,158,237,474

Now, list down the factors of 5440

1,2,4,5,8,10,16,17,20,32,34,40,64,68,80,85,136,160,170,272,320,340,544,680,1088,1360,2720,5440

Greatest Common Factor

We found the factors 474,5440 . The biggest common factor number is the GCF number.
So the greatest common factor 474,5440 is 2.

Lets's calculate LCM of 360,164

Lowest Common Multiple of 360,164 using Common Division

2	360, 164
2	180, 82
	90, 41

∴ So the LCM of the given numbers is 2 x 2 x 90 x 41 = 14760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14760

Therefore, the GCF of Fractions 474/360,5440/164 is 2/14760

Least Common Multiple of 360,164 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 360,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(360,164) = 4

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

GCF(360,164) x common factors =4 x 1 = 4

LCM(360,164) = ( 360 × 164 ) / 4

LCM(360,164) = 59040 / 4

LCM(360,164) = 14760

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FAQs on GCF of Fractions of 474/360, 5440/164

1. What is the HCF of 474,5440?

The HCF of 474,5440 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 474/360, 5440/164?

Answer: GCF of Numerators as per given numbers 474/360, 5440/164 is

GCF of Numerators i.e. for 474,5440 is 2

LCM of denominators i.e. for 360,164 is 14760.

Thus, GCF of Fractions is 2/14760.Finally, GCF of Fractions for 474/360, 5440/164 is 2/14760.