How to Find GCF of 30/33, 37/22, 861/463?

GCF of 30/33, 37/22, 861/463

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 30/33, 37/22, 861/463 i.e 1/30558 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/33, 37/22, 861/463.

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 30/33,37/22,861/463?

Given fractions are 30/33,37/22,861/463

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 30/33,37/22,861/463, numerators are 30,37,861

Denominators are 33,22,463

The GCF of 30,37,861 is 1 .

LCM of 33,22,463 is 30558.

The greatest common factor of 30/33,37/22,861/463 = [GCF of 30,37,861]/[LCM of 33,22,463]= 1/30558

Therefore, the GCF of 30/33,37/22,861/463 is 1/30558.

Greatest Common Factor of 30,37,861

To find the highest common factor of 30,37,861, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 37 are 1, 37

The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861

The HCF of 30,37,861 is 1.

Lets's calculate GCF of 30,37,861

Greatest Common Factor (GCF) of 30,37,861 By Common Division

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

Greatest Common Factor of 30,37,861 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 37

1,37

Now, list down the factors of 861

1,3,7,21,41,123,287,861

Greatest Common Factor

We found the factors 30,37,861 . The biggest common factor number is the GCF number.
So the greatest common factor 30,37,861 is 1.

Lets's calculate LCM of 33,22,463

Lowest Common Multiple of 33,22,463 using Common Division

11	33, 22, 463
	3, 2, 463

∴ So the LCM of the given numbers is 11 x 3 x 2 x 463 = 30558

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30558

Therefore, the GCF of Fractions 30/33,37/22,861/463 is 1/30558

Least Common Multiple of 33,22,463 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 33,22,463 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(33,22,463) = 1

common factors(in case of two or more numbers have common factors) = 11

GCF(33,22,463) x common factors =1 x 11 = 11

LCM(33,22,463) = ( 33 × 22 × 463 ) / 11

LCM(33,22,463) = 336138 / 11

LCM(33,22,463) = 30558

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FAQs on GCF of Fractions of 30/33, 37/22, 861/463

1. What is the HCF of 30,37,861?

The HCF of 30,37,861 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 30/33, 37/22, 861/463?

Answer: GCF of Numerators as per given numbers 30/33, 37/22, 861/463 is

GCF of Numerators i.e. for 30,37,861 is 1

LCM of denominators i.e. for 33,22,463 is 30558.

Thus, GCF of Fractions is 1/30558.Finally, GCF of Fractions for 30/33, 37/22, 861/463 is 1/30558.