How to Find GCF of 446/42, 784/719?

GCF of 446/42, 784/719

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 446/42, 784/719 i.e 2/30198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 446/42, 784/719.

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 446/42,784/719?

Given fractions are 446/42,784/719

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 446/42,784/719, numerators are 446,784

Denominators are 42,719

The GCF of 446,784 is 2 .

LCM of 42,719 is 30198.

The greatest common factor of 446/42,784/719 = [GCF of 446,784]/[LCM of 42,719]= 2/30198

Therefore, the GCF of 446/42,784/719 is 2/30198.

Greatest Common Factor of 446,784

To find the highest common factor of 446,784, we have to find the factors of both numbers and list the highest common factor.

The factors of 446 are 1, 2, 223, 446

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The HCF of 446,784 is 2.

Lets's calculate GCF of 446,784

Greatest Common Factor (GCF) of 446,784 By Common Division

2	446, 784
	223, 392

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 446,784 By Matching Biggest Common Factor Method

Now, list down the factors of 446

1,2,223,446

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Greatest Common Factor

We found the factors 446,784 . The biggest common factor number is the GCF number.
So the greatest common factor 446,784 is 2.

Lets's calculate LCM of 42,719

Lowest Common Multiple of 42,719 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 30198

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30198

Therefore, the GCF of Fractions 446/42,784/719 is 2/30198

Least Common Multiple of 42,719 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 42,719 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,719) = 1

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

GCF(42,719) x common factors =1 x 1 = 1

LCM(42,719) = ( 42 × 719 ) / 1

LCM(42,719) = 30198 / 1

LCM(42,719) = 30198

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FAQs on GCF of Fractions of 446/42, 784/719

1. What is the HCF of 446,784?

The HCF of 446,784 is 2

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 446/42, 784/719?

Answer: GCF of Numerators as per given numbers 446/42, 784/719 is

GCF of Numerators i.e. for 446,784 is 2

LCM of denominators i.e. for 42,719 is 30198.

Thus, GCF of Fractions is 2/30198.Finally, GCF of Fractions for 446/42, 784/719 is 2/30198.