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GCF of 240/289, 617/422

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 240/289, 617/422 i.e 1/121958 easily. The following is the detailed procedure to determine the greatest common factor of fractions 240/289, 617/422.

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 240/289,617/422?

Given fractions are 240/289,617/422

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 240/289,617/422, numerators are 240,617

Denominators are 289,422

The GCF of 240,617 is 1 .

LCM of 289,422 is 121958.

The greatest common factor of 240/289,617/422 = [GCF of 240,617]/[LCM of 289,422]= 1/121958

Therefore, the GCF of 240/289,617/422 is 1/121958.

Greatest Common Factor of 240,617

To find the highest common factor of 240,617, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 617 are 1, 617

The HCF of 240,617 is 1.

Lets's calculate GCF of 240,617

Greatest Common Factor (GCF) of 240,617 By Common Division

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

Greatest Common Factor of 240,617 By Matching Biggest Common Factor Method

Greatest Common Factor of 240,617 By Matching Biggest Common Factor Method

Now, list down the factors of 240

:

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

Now, list down the factors of 617

:

1,617

Greatest Common Factor

We found the factors 240,617 . The biggest common factor number is the GCF number.
So the greatest common factor 240,617 is 1.

Lets's calculate LCM of 289,422

Lowest Common Multiple of 289,422 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 121958

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/121958

Therefore, the GCF of Fractions 240/289,617/422 is 1/121958

Least Common Multiple of 289,422 with GCF Formula

Least Common Multiple of 289,422 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 289,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,422) = 1

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

GCF(289,422) x common factors =1 x 1 = 1

LCM(289,422) = ( 289 × 422 ) / 1

LCM(289,422) = 121958 / 1

LCM(289,422) = 121958


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FAQs on GCF of Fractions of 240/289, 617/422

1. What is the HCF of 240,617?

The HCF of 240,617 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 240/289, 617/422?

Answer: GCF of Numerators as per given numbers 240/289, 617/422 is

GCF of Numerators i.e. for 240,617 is 1

LCM of denominators i.e. for 289,422 is 121958.

Thus, GCF of Fractions is 1/121958.Finally, GCF of Fractions for 240/289, 617/422 is 1/121958.