How to Find GCF of 56/23, 92/19, 175/409?

GCF of 56/23, 92/19, 175/409

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 56/23, 92/19, 175/409 i.e 1/178733 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/23, 92/19, 175/409.

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 56/23,92/19,175/409?

Given fractions are 56/23,92/19,175/409

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 56/23,92/19,175/409, numerators are 56,92,175

Denominators are 23,19,409

The GCF of 56,92,175 is 1 .

LCM of 23,19,409 is 178733.

The greatest common factor of 56/23,92/19,175/409 = [GCF of 56,92,175]/[LCM of 23,19,409]= 1/178733

Therefore, the GCF of 56/23,92/19,175/409 is 1/178733.

Greatest Common Factor of 56,92,175

To find the highest common factor of 56,92,175, we have to find the factors of both numbers and list the highest common factor.

The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

The factors of 92 are 1, 2, 4, 23, 46, 92

The factors of 175 are 1, 5, 7, 25, 35, 175

The HCF of 56,92,175 is 1.

Lets's calculate GCF of 56,92,175

Greatest Common Factor (GCF) of 56,92,175 By Common Division

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

Greatest Common Factor of 56,92,175 By Matching Biggest Common Factor Method

Now, list down the factors of 56

1,2,4,7,8,14,28,56

Now, list down the factors of 92

1,2,4,23,46,92

Now, list down the factors of 175

1,5,7,25,35,175

Greatest Common Factor

We found the factors 56,92,175 . The biggest common factor number is the GCF number.
So the greatest common factor 56,92,175 is 1.

Lets's calculate LCM of 23,19,409

Lowest Common Multiple of 23,19,409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 178733

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/178733

Therefore, the GCF of Fractions 56/23,92/19,175/409 is 1/178733

Least Common Multiple of 23,19,409 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 23,19,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,19,409) = 1

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

GCF(23,19,409) x common factors =1 x 1 = 1

LCM(23,19,409) = ( 23 × 19 × 409 ) / 1

LCM(23,19,409) = 178733 / 1

LCM(23,19,409) = 178733

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FAQs on GCF of Fractions of 56/23, 92/19, 175/409

1. What is the HCF of 56,92,175?

The HCF of 56,92,175 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 56/23, 92/19, 175/409?

Answer: GCF of Numerators as per given numbers 56/23, 92/19, 175/409 is

GCF of Numerators i.e. for 56,92,175 is 1

LCM of denominators i.e. for 23,19,409 is 178733.

Thus, GCF of Fractions is 1/178733.Finally, GCF of Fractions for 56/23, 92/19, 175/409 is 1/178733.