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GCF of 289/400, 765/870

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 289/400, 765/870 i.e 17/34800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/400, 765/870.

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 289/400,765/870?

Given fractions are 289/400,765/870

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 289/400,765/870, numerators are 289,765

Denominators are 400,870

The GCF of 289,765 is 17 .

LCM of 400,870 is 34800.

The greatest common factor of 289/400,765/870 = [GCF of 289,765]/[LCM of 400,870]= 17/34800

Therefore, the GCF of 289/400,765/870 is 17/34800.

Greatest Common Factor of 289,765

To find the highest common factor of 289,765, we have to find the factors of both numbers and list the highest common factor.

The factors of 289 are 1, 17, 289

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

The HCF of 289,765 is 17.

Lets's calculate GCF of 289,765

Greatest Common Factor (GCF) of 289,765 By Common Division

17 289, 765
17, 45

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 289,765 By Matching Biggest Common Factor Method

Greatest Common Factor of 289,765 By Matching Biggest Common Factor Method

Now, list down the factors of 289

:

1,17,289

Now, list down the factors of 765

:

1,3,5,9,15,17,45,51,85,153,255,765

Greatest Common Factor

We found the factors 289,765 . The biggest common factor number is the GCF number.
So the greatest common factor 289,765 is 17.

Lets's calculate LCM of 400,870

Lowest Common Multiple of 400,870 using Common Division

2 400, 870
5 200, 435
40, 87

∴ So the LCM of the given numbers is 2 x 5 x 40 x 87 = 34800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/34800

Therefore, the GCF of Fractions 289/400,765/870 is 17/34800

Least Common Multiple of 400,870 with GCF Formula

Least Common Multiple of 400,870 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 400,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,870) = 10

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

GCF(400,870) x common factors =10 x 1 = 10

LCM(400,870) = ( 400 × 870 ) / 10

LCM(400,870) = 348000 / 10

LCM(400,870) = 34800


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FAQs on GCF of Fractions of 289/400, 765/870

1. What is the HCF of 289,765?

The HCF of 289,765 is 17

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 289/400, 765/870?

Answer: GCF of Numerators as per given numbers 289/400, 765/870 is

GCF of Numerators i.e. for 289,765 is 17

LCM of denominators i.e. for 400,870 is 34800.

Thus, GCF of Fractions is 17/34800.Finally, GCF of Fractions for 289/400, 765/870 is 17/34800.