How to Find GCF of 162/460, 805/920?

GCF of 162/460, 805/920

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 162/460, 805/920 i.e 1/920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/460, 805/920.

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 162/460,805/920?

Given fractions are 162/460,805/920

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 162/460,805/920, numerators are 162,805

Denominators are 460,920

The GCF of 162,805 is 1 .

LCM of 460,920 is 920.

The greatest common factor of 162/460,805/920 = [GCF of 162,805]/[LCM of 460,920]= 1/920

Therefore, the GCF of 162/460,805/920 is 1/920.

Greatest Common Factor of 162,805

To find the highest common factor of 162,805, we have to find the factors of both numbers and list the highest common factor.

The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162

The factors of 805 are 1, 5, 7, 23, 35, 115, 161, 805

The HCF of 162,805 is 1.

Lets's calculate GCF of 162,805

Greatest Common Factor (GCF) of 162,805 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 162,805 By Matching Biggest Common Factor Method

Now, list down the factors of 162

1,2,3,6,9,18,27,54,81,162

Now, list down the factors of 805

1,5,7,23,35,115,161,805

Greatest Common Factor

We found the factors 162,805 . The biggest common factor number is the GCF number.
So the greatest common factor 162,805 is 1.

Lets's calculate LCM of 460,920

Lowest Common Multiple of 460,920 using Common Division

2	460, 920
2	230, 460
5	115, 230
23	23, 46
	1, 2

∴ So the LCM of the given numbers is 2 x 2 x 5 x 23 x 1 x 2 = 920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/920

Therefore, the GCF of Fractions 162/460,805/920 is 1/920

Least Common Multiple of 460,920 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 460,920 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(460,920) = 460

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

GCF(460,920) x common factors =460 x 1 = 460

LCM(460,920) = ( 460 × 920 ) / 460

LCM(460,920) = 423200 / 460

LCM(460,920) = 920

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FAQs on GCF of Fractions of 162/460, 805/920

1. What is the HCF of 162,805?

The HCF of 162,805 is 1

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 162/460, 805/920?

Answer: GCF of Numerators as per given numbers 162/460, 805/920 is

GCF of Numerators i.e. for 162,805 is 1

LCM of denominators i.e. for 460,920 is 920.

Thus, GCF of Fractions is 1/920.Finally, GCF of Fractions for 162/460, 805/920 is 1/920.