How to Find GCF of 23/48, 705/58, 870/415?

GCF of 23/48, 705/58, 870/415

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 23/48, 705/58, 870/415 i.e 1/577680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/48, 705/58, 870/415.

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 23/48,705/58,870/415?

Given fractions are 23/48,705/58,870/415

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 23/48,705/58,870/415, numerators are 23,705,870

Denominators are 48,58,415

The GCF of 23,705,870 is 1 .

LCM of 48,58,415 is 577680.

The greatest common factor of 23/48,705/58,870/415 = [GCF of 23,705,870]/[LCM of 48,58,415]= 1/577680

Therefore, the GCF of 23/48,705/58,870/415 is 1/577680.

Greatest Common Factor of 23,705,870

To find the highest common factor of 23,705,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 23 are 1, 23

The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705

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

The HCF of 23,705,870 is 1.

Lets's calculate GCF of 23,705,870

Greatest Common Factor (GCF) of 23,705,870 By Common Division

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

Greatest Common Factor of 23,705,870 By Matching Biggest Common Factor Method

Now, list down the factors of 23

1,23

Now, list down the factors of 705

1,3,5,15,47,141,235,705

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 23,705,870 . The biggest common factor number is the GCF number.
So the greatest common factor 23,705,870 is 1.

Lets's calculate LCM of 48,58,415

Lowest Common Multiple of 48,58,415 using Common Division

2	48, 58, 415
	24, 29, 415

∴ So the LCM of the given numbers is 2 x 24 x 29 x 415 = 577680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/577680

Therefore, the GCF of Fractions 23/48,705/58,870/415 is 1/577680

Least Common Multiple of 48,58,415 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 48,58,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(48,58,415) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(48,58,415) x common factors =1 x 2 = 2

LCM(48,58,415) = ( 48 × 58 × 415 ) / 2

LCM(48,58,415) = 1155360 / 2

LCM(48,58,415) = 577680

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 23/48, 705/58, 870/415

1. What is the HCF of 23,705,870?

The HCF of 23,705,870 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 23/48, 705/58, 870/415?

Answer: GCF of Numerators as per given numbers 23/48, 705/58, 870/415 is

GCF of Numerators i.e. for 23,705,870 is 1

LCM of denominators i.e. for 48,58,415 is 577680.

Thus, GCF of Fractions is 1/577680.Finally, GCF of Fractions for 23/48, 705/58, 870/415 is 1/577680.