How to Find GCF of 240/17, 870/562?

GCF of 240/17, 870/562

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 240/17, 870/562 i.e 30/9554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 240/17, 870/562.

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 240/17,870/562?

Given fractions are 240/17,870/562

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 240/17,870/562, numerators are 240,870

Denominators are 17,562

The GCF of 240,870 is 30 .

LCM of 17,562 is 9554.

The greatest common factor of 240/17,870/562 = [GCF of 240,870]/[LCM of 17,562]= 30/9554

Therefore, the GCF of 240/17,870/562 is 30/9554.

Greatest Common Factor of 240,870

To find the highest common factor of 240,870, 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 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 240,870 is 30.

Lets's calculate GCF of 240,870

Greatest Common Factor (GCF) of 240,870 By Common Division

2	240, 870
3	120, 435
5	40, 145
	8, 29

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 240,870 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 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 240,870 . The biggest common factor number is the GCF number.
So the greatest common factor 240,870 is 30.

Lets's calculate LCM of 17,562

Lowest Common Multiple of 17,562 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9554

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/9554

Therefore, the GCF of Fractions 240/17,870/562 is 30/9554

Least Common Multiple of 17,562 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 17,562 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,562) = 1

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

GCF(17,562) x common factors =1 x 1 = 1

LCM(17,562) = ( 17 × 562 ) / 1

LCM(17,562) = 9554 / 1

LCM(17,562) = 9554

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FAQs on GCF of Fractions of 240/17, 870/562

1. What is the HCF of 240,870?

The HCF of 240,870 is 30

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 240/17, 870/562?

Answer: GCF of Numerators as per given numbers 240/17, 870/562 is

GCF of Numerators i.e. for 240,870 is 30

LCM of denominators i.e. for 17,562 is 9554.

Thus, GCF of Fractions is 30/9554.Finally, GCF of Fractions for 240/17, 870/562 is 30/9554.