How to Find GCF of 992/23, 420/815?

GCF of 992/23, 420/815

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 992/23, 420/815 i.e 4/18745 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/23, 420/815.

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 992/23,420/815?

Given fractions are 992/23,420/815

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 992/23,420/815, numerators are 992,420

Denominators are 23,815

The GCF of 992,420 is 4 .

LCM of 23,815 is 18745.

The greatest common factor of 992/23,420/815 = [GCF of 992,420]/[LCM of 23,815]= 4/18745

Therefore, the GCF of 992/23,420/815 is 4/18745.

Greatest Common Factor of 992,420

To find the highest common factor of 992,420, we have to find the factors of both numbers and list the highest common factor.

The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 992,420 is 4.

Lets's calculate GCF of 992,420

Greatest Common Factor (GCF) of 992,420 By Common Division

2	992, 420
2	496, 210
	248, 105

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 992,420 By Matching Biggest Common Factor Method

Now, list down the factors of 992

1,2,4,8,16,31,32,62,124,248,496,992

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 992,420 . The biggest common factor number is the GCF number.
So the greatest common factor 992,420 is 4.

Lets's calculate LCM of 23,815

Lowest Common Multiple of 23,815 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 18745

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/18745

Therefore, the GCF of Fractions 992/23,420/815 is 4/18745

Least Common Multiple of 23,815 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 23,815 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,815) = 1

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

GCF(23,815) x common factors =1 x 1 = 1

LCM(23,815) = ( 23 × 815 ) / 1

LCM(23,815) = 18745 / 1

LCM(23,815) = 18745

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FAQs on GCF of Fractions of 992/23, 420/815

1. What is the HCF of 992,420?

The HCF of 992,420 is 4

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 992/23, 420/815?

Answer: GCF of Numerators as per given numbers 992/23, 420/815 is

GCF of Numerators i.e. for 992,420 is 4

LCM of denominators i.e. for 23,815 is 18745.

Thus, GCF of Fractions is 4/18745.Finally, GCF of Fractions for 992/23, 420/815 is 4/18745.