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GCF of 724/47, 120/209

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 724/47, 120/209 i.e 4/9823 easily. The following is the detailed procedure to determine the greatest common factor of fractions 724/47, 120/209.

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 724/47,120/209?

Given fractions are 724/47,120/209

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 724/47,120/209, numerators are 724,120

Denominators are 47,209

The GCF of 724,120 is 4 .

LCM of 47,209 is 9823.

The greatest common factor of 724/47,120/209 = [GCF of 724,120]/[LCM of 47,209]= 4/9823

Therefore, the GCF of 724/47,120/209 is 4/9823.

Greatest Common Factor of 724,120

To find the highest common factor of 724,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 724 are 1, 2, 4, 181, 362, 724

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

The HCF of 724,120 is 4.

Lets's calculate GCF of 724,120

Greatest Common Factor (GCF) of 724,120 By Common Division

2 724, 120
2 362, 60
181, 30

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 724,120 By Matching Biggest Common Factor Method

Greatest Common Factor of 724,120 By Matching Biggest Common Factor Method

Now, list down the factors of 724

:

1,2,4,181,362,724

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 724,120 . The biggest common factor number is the GCF number.
So the greatest common factor 724,120 is 4.

Lets's calculate LCM of 47,209

Lowest Common Multiple of 47,209 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9823

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/9823

Therefore, the GCF of Fractions 724/47,120/209 is 4/9823

Least Common Multiple of 47,209 with GCF Formula

Least Common Multiple of 47,209 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 47,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,209) = 1

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

GCF(47,209) x common factors =1 x 1 = 1

LCM(47,209) = ( 47 × 209 ) / 1

LCM(47,209) = 9823 / 1

LCM(47,209) = 9823


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FAQs on GCF of Fractions of 724/47, 120/209

1. What is the HCF of 724,120?

The HCF of 724,120 is 4

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 724/47, 120/209?

Answer: GCF of Numerators as per given numbers 724/47, 120/209 is

GCF of Numerators i.e. for 724,120 is 4

LCM of denominators i.e. for 47,209 is 9823.

Thus, GCF of Fractions is 4/9823.Finally, GCF of Fractions for 724/47, 120/209 is 4/9823.