How to Find GCF of 416/384, 684/377?

GCF of 416/384, 684/377

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 416/384, 684/377 i.e 4/144768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/384, 684/377.

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 416/384,684/377?

Given fractions are 416/384,684/377

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 416/384,684/377, numerators are 416,684

Denominators are 384,377

The GCF of 416,684 is 4 .

LCM of 384,377 is 144768.

The greatest common factor of 416/384,684/377 = [GCF of 416,684]/[LCM of 384,377]= 4/144768

Therefore, the GCF of 416/384,684/377 is 4/144768.

Greatest Common Factor of 416,684

To find the highest common factor of 416,684, 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 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

The HCF of 416,684 is 4.

Lets's calculate GCF of 416,684

Greatest Common Factor (GCF) of 416,684 By Common Division

2	416, 684
2	208, 342
	104, 171

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 416,684 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 684

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Greatest Common Factor

We found the factors 416,684 . The biggest common factor number is the GCF number.
So the greatest common factor 416,684 is 4.

Lets's calculate LCM of 384,377

Lowest Common Multiple of 384,377 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 144768

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/144768

Therefore, the GCF of Fractions 416/384,684/377 is 4/144768

Least Common Multiple of 384,377 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 384,377 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(384,377) = 1

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

GCF(384,377) x common factors =1 x 1 = 1

LCM(384,377) = ( 384 × 377 ) / 1

LCM(384,377) = 144768 / 1

LCM(384,377) = 144768

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FAQs on GCF of Fractions of 416/384, 684/377

1. What is the HCF of 416,684?

The HCF of 416,684 is 4

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 416/384, 684/377?

Answer: GCF of Numerators as per given numbers 416/384, 684/377 is

GCF of Numerators i.e. for 416,684 is 4

LCM of denominators i.e. for 384,377 is 144768.

Thus, GCF of Fractions is 4/144768.Finally, GCF of Fractions for 416/384, 684/377 is 4/144768.