How to Find GCF of 55/71, 417/25, 404/120?

GCF of 55/71, 417/25, 404/120

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 55/71, 417/25, 404/120 i.e 1/42600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 55/71, 417/25, 404/120.

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 55/71,417/25,404/120?

Given fractions are 55/71,417/25,404/120

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 55/71,417/25,404/120, numerators are 55,417,404

Denominators are 71,25,120

The GCF of 55,417,404 is 1 .

LCM of 71,25,120 is 42600.

The greatest common factor of 55/71,417/25,404/120 = [GCF of 55,417,404]/[LCM of 71,25,120]= 1/42600

Therefore, the GCF of 55/71,417/25,404/120 is 1/42600.

Greatest Common Factor of 55,417,404

To find the highest common factor of 55,417,404, we have to find the factors of both numbers and list the highest common factor.

The factors of 55 are 1, 5, 11, 55

The factors of 417 are 1, 3, 139, 417

The factors of 404 are 1, 2, 4, 101, 202, 404

The HCF of 55,417,404 is 1.

Lets's calculate GCF of 55,417,404

Greatest Common Factor (GCF) of 55,417,404 By Common Division

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

Greatest Common Factor of 55,417,404 By Matching Biggest Common Factor Method

Now, list down the factors of 55

1,5,11,55

Now, list down the factors of 417

1,3,139,417

Now, list down the factors of 404

1,2,4,101,202,404

Greatest Common Factor

We found the factors 55,417,404 . The biggest common factor number is the GCF number.
So the greatest common factor 55,417,404 is 1.

Lets's calculate LCM of 71,25,120

Lowest Common Multiple of 71,25,120 using Common Division

5	71, 25, 120
	71, 5, 24

∴ So the LCM of the given numbers is 5 x 71 x 5 x 24 = 42600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42600

Therefore, the GCF of Fractions 55/71,417/25,404/120 is 1/42600

Least Common Multiple of 71,25,120 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 71,25,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(71,25,120) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(71,25,120) x common factors =1 x 5 = 5

LCM(71,25,120) = ( 71 × 25 × 120 ) / 5

LCM(71,25,120) = 213000 / 5

LCM(71,25,120) = 42600

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FAQs on GCF of Fractions of 55/71, 417/25, 404/120

1. What is the HCF of 55,417,404?

The HCF of 55,417,404 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 55/71, 417/25, 404/120?

Answer: GCF of Numerators as per given numbers 55/71, 417/25, 404/120 is

GCF of Numerators i.e. for 55,417,404 is 1

LCM of denominators i.e. for 71,25,120 is 42600.

Thus, GCF of Fractions is 1/42600.Finally, GCF of Fractions for 55/71, 417/25, 404/120 is 1/42600.