How to Find GCF of 408/709, 480/685?

GCF of 408/709, 480/685

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 408/709, 480/685 i.e 24/485665 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/709, 480/685.

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 408/709,480/685?

Given fractions are 408/709,480/685

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 408/709,480/685, numerators are 408,480

Denominators are 709,685

The GCF of 408,480 is 24 .

LCM of 709,685 is 485665.

The greatest common factor of 408/709,480/685 = [GCF of 408,480]/[LCM of 709,685]= 24/485665

Therefore, the GCF of 408/709,480/685 is 24/485665.

Greatest Common Factor of 408,480

To find the highest common factor of 408,480, we have to find the factors of both numbers and list the highest common factor.

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

The HCF of 408,480 is 24.

Lets's calculate GCF of 408,480

Greatest Common Factor (GCF) of 408,480 By Common Division

2	408, 480
2	204, 240
2	102, 120
3	51, 60
	17, 20

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 408,480 By Matching Biggest Common Factor Method

Now, list down the factors of 408

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Now, list down the factors of 480

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480

Greatest Common Factor

We found the factors 408,480 . The biggest common factor number is the GCF number.
So the greatest common factor 408,480 is 24.

Lets's calculate LCM of 709,685

Lowest Common Multiple of 709,685 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 485665

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/485665

Therefore, the GCF of Fractions 408/709,480/685 is 24/485665

Least Common Multiple of 709,685 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 709,685 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(709,685) = 1

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

GCF(709,685) x common factors =1 x 1 = 1

LCM(709,685) = ( 709 × 685 ) / 1

LCM(709,685) = 485665 / 1

LCM(709,685) = 485665

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FAQs on GCF of Fractions of 408/709, 480/685

1. What is the HCF of 408,480?

The HCF of 408,480 is 24

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 408/709, 480/685?

Answer: GCF of Numerators as per given numbers 408/709, 480/685 is

GCF of Numerators i.e. for 408,480 is 24

LCM of denominators i.e. for 709,685 is 485665.

Thus, GCF of Fractions is 24/485665.Finally, GCF of Fractions for 408/709, 480/685 is 24/485665.