How to Find GCF of 416/74, 784/797?

GCF of 416/74, 784/797

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 416/74, 784/797 i.e 16/58978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/74, 784/797.

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 416/74,784/797?

Given fractions are 416/74,784/797

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 416/74,784/797, numerators are 416,784

Denominators are 74,797

The GCF of 416,784 is 16 .

LCM of 74,797 is 58978.

The greatest common factor of 416/74,784/797 = [GCF of 416,784]/[LCM of 74,797]= 16/58978

Therefore, the GCF of 416/74,784/797 is 16/58978.

Greatest Common Factor of 416,784

To find the highest common factor of 416,784, we have to find the factors of both numbers and list the highest common factor.

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

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

The HCF of 416,784 is 16.

Lets's calculate GCF of 416,784

Greatest Common Factor (GCF) of 416,784 By Common Division

2	416, 784
2	208, 392
2	104, 196
2	52, 98
	26, 49

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 416,784 By Matching Biggest Common Factor Method

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

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 416,784 . The biggest common factor number is the GCF number.
So the greatest common factor 416,784 is 16.

Lets's calculate LCM of 74,797

Lowest Common Multiple of 74,797 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 58978

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/58978

Therefore, the GCF of Fractions 416/74,784/797 is 16/58978

Least Common Multiple of 74,797 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 74,797 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,797) = 1

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

GCF(74,797) x common factors =1 x 1 = 1

LCM(74,797) = ( 74 × 797 ) / 1

LCM(74,797) = 58978 / 1

LCM(74,797) = 58978

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FAQs on GCF of Fractions of 416/74, 784/797

1. What is the HCF of 416,784?

The HCF of 416,784 is 16

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 416/74, 784/797?

Answer: GCF of Numerators as per given numbers 416/74, 784/797 is

GCF of Numerators i.e. for 416,784 is 16

LCM of denominators i.e. for 74,797 is 58978.

Thus, GCF of Fractions is 16/58978.Finally, GCF of Fractions for 416/74, 784/797 is 16/58978.