How to Find GCF of 720/54, 340/7476?

GCF of 720/54, 340/7476

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 720/54, 340/7476 i.e 20/67284 easily. The following is the detailed procedure to determine the greatest common factor of fractions 720/54, 340/7476.

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 720/54,340/7476?

Given fractions are 720/54,340/7476

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 720/54,340/7476, numerators are 720,340

Denominators are 54,7476

The GCF of 720,340 is 20 .

LCM of 54,7476 is 67284.

The greatest common factor of 720/54,340/7476 = [GCF of 720,340]/[LCM of 54,7476]= 20/67284

Therefore, the GCF of 720/54,340/7476 is 20/67284.

Greatest Common Factor of 720,340

To find the highest common factor of 720,340, we have to find the factors of both numbers and list the highest common factor.

The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

The HCF of 720,340 is 20.

Lets's calculate GCF of 720,340

Greatest Common Factor (GCF) of 720,340 By Common Division

2	720, 340
2	360, 170
5	180, 85
	36, 17

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

Greatest Common Factor of 720,340 By Matching Biggest Common Factor Method

Now, list down the factors of 720

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720

Now, list down the factors of 340

1,2,4,5,10,17,20,34,68,85,170,340

Greatest Common Factor

We found the factors 720,340 . The biggest common factor number is the GCF number.
So the greatest common factor 720,340 is 20.

Lets's calculate LCM of 54,7476

Lowest Common Multiple of 54,7476 using Common Division

2	54, 7476
3	27, 3738
	9, 1246

∴ So the LCM of the given numbers is 2 x 3 x 9 x 1246 = 67284

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/67284

Therefore, the GCF of Fractions 720/54,340/7476 is 20/67284

Least Common Multiple of 54,7476 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 54,7476 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,7476) = 6

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

GCF(54,7476) x common factors =6 x 1 = 6

LCM(54,7476) = ( 54 × 7476 ) / 6

LCM(54,7476) = 403704 / 6

LCM(54,7476) = 67284

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FAQs on GCF of Fractions of 720/54, 340/7476

1. What is the HCF of 720,340?

The HCF of 720,340 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 720/54, 340/7476?

Answer: GCF of Numerators as per given numbers 720/54, 340/7476 is

GCF of Numerators i.e. for 720,340 is 20

LCM of denominators i.e. for 54,7476 is 67284.

Thus, GCF of Fractions is 20/67284.Finally, GCF of Fractions for 720/54, 340/7476 is 20/67284.