How to Find GCF of 360/390, 109/742?

GCF of 360/390, 109/742

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 360/390, 109/742 i.e 1/144690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/390, 109/742.

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 360/390,109/742?

Given fractions are 360/390,109/742

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 360/390,109/742, numerators are 360,109

Denominators are 390,742

The GCF of 360,109 is 1 .

LCM of 390,742 is 144690.

The greatest common factor of 360/390,109/742 = [GCF of 360,109]/[LCM of 390,742]= 1/144690

Therefore, the GCF of 360/390,109/742 is 1/144690.

Greatest Common Factor of 360,109

To find the highest common factor of 360,109, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 109 are 1, 109

The HCF of 360,109 is 1.

Lets's calculate GCF of 360,109

Greatest Common Factor (GCF) of 360,109 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 360,109 By Matching Biggest Common Factor Method

Now, list down the factors of 360

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

Now, list down the factors of 109

1,109

Greatest Common Factor

We found the factors 360,109 . The biggest common factor number is the GCF number.
So the greatest common factor 360,109 is 1.

Lets's calculate LCM of 390,742

Lowest Common Multiple of 390,742 using Common Division

2	390, 742
	195, 371

∴ So the LCM of the given numbers is 2 x 195 x 371 = 144690

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/144690

Therefore, the GCF of Fractions 360/390,109/742 is 1/144690

Least Common Multiple of 390,742 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 390,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(390,742) = 2

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

GCF(390,742) x common factors =2 x 1 = 2

LCM(390,742) = ( 390 × 742 ) / 2

LCM(390,742) = 289380 / 2

LCM(390,742) = 144690

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FAQs on GCF of Fractions of 360/390, 109/742

1. What is the HCF of 360,109?

The HCF of 360,109 is 1

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 360/390, 109/742?

Answer: GCF of Numerators as per given numbers 360/390, 109/742 is

GCF of Numerators i.e. for 360,109 is 1

LCM of denominators i.e. for 390,742 is 144690.

Thus, GCF of Fractions is 1/144690.Finally, GCF of Fractions for 360/390, 109/742 is 1/144690.