How to Find GCF of 225/470, 120/661?

GCF of 225/470, 120/661

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 225/470, 120/661 i.e 15/310670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 225/470, 120/661.

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 225/470,120/661?

Given fractions are 225/470,120/661

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 225/470,120/661, numerators are 225,120

Denominators are 470,661

The GCF of 225,120 is 15 .

LCM of 470,661 is 310670.

The greatest common factor of 225/470,120/661 = [GCF of 225,120]/[LCM of 470,661]= 15/310670

Therefore, the GCF of 225/470,120/661 is 15/310670.

Greatest Common Factor of 225,120

To find the highest common factor of 225,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225

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

The HCF of 225,120 is 15.

Lets's calculate GCF of 225,120

Greatest Common Factor (GCF) of 225,120 By Common Division

3	225, 120
5	75, 40
	15, 8

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 225,120 By Matching Biggest Common Factor Method

Now, list down the factors of 225

1,3,5,9,15,25,45,75,225

Now, list down the factors of 120

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

Greatest Common Factor

We found the factors 225,120 . The biggest common factor number is the GCF number.
So the greatest common factor 225,120 is 15.

Lets's calculate LCM of 470,661

Lowest Common Multiple of 470,661 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 310670

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/310670

Therefore, the GCF of Fractions 225/470,120/661 is 15/310670

Least Common Multiple of 470,661 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 470,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,661) = 1

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

GCF(470,661) x common factors =1 x 1 = 1

LCM(470,661) = ( 470 × 661 ) / 1

LCM(470,661) = 310670 / 1

LCM(470,661) = 310670

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 225/470, 120/661

1. What is the HCF of 225,120?

The HCF of 225,120 is 15

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 225/470, 120/661?

Answer: GCF of Numerators as per given numbers 225/470, 120/661 is

GCF of Numerators i.e. for 225,120 is 15

LCM of denominators i.e. for 470,661 is 310670.

Thus, GCF of Fractions is 15/310670.Finally, GCF of Fractions for 225/470, 120/661 is 15/310670.