How to Find GCF of 900/34, 440/272?

GCF of 900/34, 440/272

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 900/34, 440/272 i.e 20/272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/34, 440/272.

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 900/34,440/272?

Given fractions are 900/34,440/272

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 900/34,440/272, numerators are 900,440

Denominators are 34,272

The GCF of 900,440 is 20 .

LCM of 34,272 is 272.

The greatest common factor of 900/34,440/272 = [GCF of 900,440]/[LCM of 34,272]= 20/272

Therefore, the GCF of 900/34,440/272 is 20/272.

Greatest Common Factor of 900,440

To find the highest common factor of 900,440, we have to find the factors of both numbers and list the highest common factor.

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440

The HCF of 900,440 is 20.

Lets's calculate GCF of 900,440

Greatest Common Factor (GCF) of 900,440 By Common Division

2	900, 440
2	450, 220
5	225, 110
	45, 22

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 900,440 By Matching Biggest Common Factor Method

Now, list down the factors of 900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

Now, list down the factors of 440

1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440

Greatest Common Factor

We found the factors 900,440 . The biggest common factor number is the GCF number.
So the greatest common factor 900,440 is 20.

Lets's calculate LCM of 34,272

Lowest Common Multiple of 34,272 using Common Division

2	34, 272
17	17, 136
	1, 8

∴ So the LCM of the given numbers is 2 x 17 x 1 x 8 = 272

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/272

Therefore, the GCF of Fractions 900/34,440/272 is 20/272

Least Common Multiple of 34,272 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 34,272 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,272) = 34

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

GCF(34,272) x common factors =34 x 1 = 34

LCM(34,272) = ( 34 × 272 ) / 34

LCM(34,272) = 9248 / 34

LCM(34,272) = 272

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FAQs on GCF of Fractions of 900/34, 440/272

1. What is the HCF of 900,440?

The HCF of 900,440 is 20

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 900/34, 440/272?

Answer: GCF of Numerators as per given numbers 900/34, 440/272 is

GCF of Numerators i.e. for 900,440 is 20

LCM of denominators i.e. for 34,272 is 272.

Thus, GCF of Fractions is 20/272.Finally, GCF of Fractions for 900/34, 440/272 is 20/272.