How to Find GCF of 416/59, 392/876?

GCF of 416/59, 392/876

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 416/59, 392/876 i.e 8/51684 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/59, 392/876.

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 416/59,392/876?

Given fractions are 416/59,392/876

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 416/59,392/876, numerators are 416,392

Denominators are 59,876

The GCF of 416,392 is 8 .

LCM of 59,876 is 51684.

The greatest common factor of 416/59,392/876 = [GCF of 416,392]/[LCM of 59,876]= 8/51684

Therefore, the GCF of 416/59,392/876 is 8/51684.

Greatest Common Factor of 416,392

To find the highest common factor of 416,392, 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 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392

The HCF of 416,392 is 8.

Lets's calculate GCF of 416,392

Greatest Common Factor (GCF) of 416,392 By Common Division

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

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 416,392 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 392

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

Greatest Common Factor

We found the factors 416,392 . The biggest common factor number is the GCF number.
So the greatest common factor 416,392 is 8.

Lets's calculate LCM of 59,876

Lowest Common Multiple of 59,876 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 51684

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/51684

Therefore, the GCF of Fractions 416/59,392/876 is 8/51684

Least Common Multiple of 59,876 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 59,876 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,876) = 1

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

GCF(59,876) x common factors =1 x 1 = 1

LCM(59,876) = ( 59 × 876 ) / 1

LCM(59,876) = 51684 / 1

LCM(59,876) = 51684

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FAQs on GCF of Fractions of 416/59, 392/876

1. What is the HCF of 416,392?

The HCF of 416,392 is 8

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 416/59, 392/876?

Answer: GCF of Numerators as per given numbers 416/59, 392/876 is

GCF of Numerators i.e. for 416,392 is 8

LCM of denominators i.e. for 59,876 is 51684.

Thus, GCF of Fractions is 8/51684.Finally, GCF of Fractions for 416/59, 392/876 is 8/51684.