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GCF of 120/85, 897/384

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 120/85, 897/384 i.e 3/32640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/85, 897/384.

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 120/85,897/384?

Given fractions are 120/85,897/384

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 120/85,897/384, numerators are 120,897

Denominators are 85,384

The GCF of 120,897 is 3 .

LCM of 85,384 is 32640.

The greatest common factor of 120/85,897/384 = [GCF of 120,897]/[LCM of 85,384]= 3/32640

Therefore, the GCF of 120/85,897/384 is 3/32640.

Greatest Common Factor of 120,897

To find the highest common factor of 120,897, we have to find the factors of both numbers and list the highest common factor.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897

The HCF of 120,897 is 3.

Lets's calculate GCF of 120,897

Greatest Common Factor (GCF) of 120,897 By Common Division

3 120, 897
40, 299

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 120,897 By Matching Biggest Common Factor Method

Greatest Common Factor of 120,897 By Matching Biggest Common Factor Method

Now, list down the factors of 120

:

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Now, list down the factors of 897

:

1,3,13,23,39,69,299,897

Greatest Common Factor

We found the factors 120,897 . The biggest common factor number is the GCF number.
So the greatest common factor 120,897 is 3.

Lets's calculate LCM of 85,384

Lowest Common Multiple of 85,384 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 32640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/32640

Therefore, the GCF of Fractions 120/85,897/384 is 3/32640

Least Common Multiple of 85,384 with GCF Formula

Least Common Multiple of 85,384 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 85,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(85,384) = 1

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

GCF(85,384) x common factors =1 x 1 = 1

LCM(85,384) = ( 85 × 384 ) / 1

LCM(85,384) = 32640 / 1

LCM(85,384) = 32640


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FAQs on GCF of Fractions of 120/85, 897/384

1. What is the HCF of 120,897?

The HCF of 120,897 is 3

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 120/85, 897/384?

Answer: GCF of Numerators as per given numbers 120/85, 897/384 is

GCF of Numerators i.e. for 120,897 is 3

LCM of denominators i.e. for 85,384 is 32640.

Thus, GCF of Fractions is 3/32640.Finally, GCF of Fractions for 120/85, 897/384 is 3/32640.