How to Find GCF of 61/60, 598/30, 461/133?

GCF of 61/60, 598/30, 461/133

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 61/60, 598/30, 461/133 i.e 1/7980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/60, 598/30, 461/133.

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 61/60,598/30,461/133?

Given fractions are 61/60,598/30,461/133

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 61/60,598/30,461/133, numerators are 61,598,461

Denominators are 60,30,133

The GCF of 61,598,461 is 1 .

LCM of 60,30,133 is 7980.

The greatest common factor of 61/60,598/30,461/133 = [GCF of 61,598,461]/[LCM of 60,30,133]= 1/7980

Therefore, the GCF of 61/60,598/30,461/133 is 1/7980.

Greatest Common Factor of 61,598,461

To find the highest common factor of 61,598,461, we have to find the factors of both numbers and list the highest common factor.

The factors of 61 are 1, 61

The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598

The factors of 461 are 1, 461

The HCF of 61,598,461 is 1.

Lets's calculate GCF of 61,598,461

Greatest Common Factor (GCF) of 61,598,461 By Common Division

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

Greatest Common Factor of 61,598,461 By Matching Biggest Common Factor Method

Now, list down the factors of 61

1,61

Now, list down the factors of 598

1,2,13,23,26,46,299,598

Now, list down the factors of 461

1,461

Greatest Common Factor

We found the factors 61,598,461 . The biggest common factor number is the GCF number.
So the greatest common factor 61,598,461 is 1.

Lets's calculate LCM of 60,30,133

Lowest Common Multiple of 60,30,133 using Common Division

2	60, 30, 133
3	30, 15, 133
5	10, 5, 133
	2, 1, 133

∴ So the LCM of the given numbers is 2 x 3 x 5 x 2 x 1 x 133 = 7980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7980

Therefore, the GCF of Fractions 61/60,598/30,461/133 is 1/7980

Least Common Multiple of 60,30,133 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 60,30,133 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(60,30,133) = 1

common factors(in case of two or more numbers have common factors) = 30

GCF(60,30,133) x common factors =1 x 30 = 30

LCM(60,30,133) = ( 60 × 30 × 133 ) / 30

LCM(60,30,133) = 239400 / 30

LCM(60,30,133) = 7980

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FAQs on GCF of Fractions of 61/60, 598/30, 461/133

1. What is the HCF of 61,598,461?

The HCF of 61,598,461 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 61/60, 598/30, 461/133?

Answer: GCF of Numerators as per given numbers 61/60, 598/30, 461/133 is

GCF of Numerators i.e. for 61,598,461 is 1

LCM of denominators i.e. for 60,30,133 is 7980.

Thus, GCF of Fractions is 1/7980.Finally, GCF of Fractions for 61/60, 598/30, 461/133 is 1/7980.