How to Find GCF of 60/15, 182/49, 419/596?

GCF of 60/15, 182/49, 419/596

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 60/15, 182/49, 419/596 i.e 1/438060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/15, 182/49, 419/596.

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 60/15,182/49,419/596?

Given fractions are 60/15,182/49,419/596

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 60/15,182/49,419/596, numerators are 60,182,419

Denominators are 15,49,596

The GCF of 60,182,419 is 1 .

LCM of 15,49,596 is 438060.

The greatest common factor of 60/15,182/49,419/596 = [GCF of 60,182,419]/[LCM of 15,49,596]= 1/438060

Therefore, the GCF of 60/15,182/49,419/596 is 1/438060.

Greatest Common Factor of 60,182,419

To find the highest common factor of 60,182,419, we have to find the factors of both numbers and list the highest common factor.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182

The factors of 419 are 1, 419

The HCF of 60,182,419 is 1.

Lets's calculate GCF of 60,182,419

Greatest Common Factor (GCF) of 60,182,419 By Common Division

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

Greatest Common Factor of 60,182,419 By Matching Biggest Common Factor Method

Now, list down the factors of 60

1,2,3,4,5,6,10,12,15,20,30,60

Now, list down the factors of 182

1,2,7,13,14,26,91,182

Now, list down the factors of 419

1,419

Greatest Common Factor

We found the factors 60,182,419 . The biggest common factor number is the GCF number.
So the greatest common factor 60,182,419 is 1.

Lets's calculate LCM of 15,49,596

Lowest Common Multiple of 15,49,596 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 438060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/438060

Therefore, the GCF of Fractions 60/15,182/49,419/596 is 1/438060

Least Common Multiple of 15,49,596 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 15,49,596 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(15,49,596) = 1

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

GCF(15,49,596) x common factors =1 x 1 = 1

LCM(15,49,596) = ( 15 × 49 × 596 ) / 1

LCM(15,49,596) = 438060 / 1

LCM(15,49,596) = 438060

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FAQs on GCF of Fractions of 60/15, 182/49, 419/596

1. What is the HCF of 60,182,419?

The HCF of 60,182,419 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 60/15, 182/49, 419/596?

Answer: GCF of Numerators as per given numbers 60/15, 182/49, 419/596 is

GCF of Numerators i.e. for 60,182,419 is 1

LCM of denominators i.e. for 15,49,596 is 438060.

Thus, GCF of Fractions is 1/438060.Finally, GCF of Fractions for 60/15, 182/49, 419/596 is 1/438060.