How to Find GCF of 416/409, 1608/716?

GCF of 416/409, 1608/716

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 416/409, 1608/716 i.e 8/292844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/409, 1608/716.

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 416/409,1608/716?

Given fractions are 416/409,1608/716

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 416/409,1608/716, numerators are 416,1608

Denominators are 409,716

The GCF of 416,1608 is 8 .

LCM of 409,716 is 292844.

The greatest common factor of 416/409,1608/716 = [GCF of 416,1608]/[LCM of 409,716]= 8/292844

Therefore, the GCF of 416/409,1608/716 is 8/292844.

Greatest Common Factor of 416,1608

To find the highest common factor of 416,1608, 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 1608 are 1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608

The HCF of 416,1608 is 8.

Lets's calculate GCF of 416,1608

Greatest Common Factor (GCF) of 416,1608 By Common Division

2	416, 1608
2	208, 804
2	104, 402
	52, 201

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

Greatest Common Factor of 416,1608 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 1608

1,2,3,4,6,8,12,24,67,134,201,268,402,536,804,1608

Greatest Common Factor

We found the factors 416,1608 . The biggest common factor number is the GCF number.
So the greatest common factor 416,1608 is 8.

Lets's calculate LCM of 409,716

Lowest Common Multiple of 409,716 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 292844

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/292844

Therefore, the GCF of Fractions 416/409,1608/716 is 8/292844

Least Common Multiple of 409,716 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 409,716 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(409,716) = 1

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

GCF(409,716) x common factors =1 x 1 = 1

LCM(409,716) = ( 409 × 716 ) / 1

LCM(409,716) = 292844 / 1

LCM(409,716) = 292844

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FAQs on GCF of Fractions of 416/409, 1608/716

1. What is the HCF of 416,1608?

The HCF of 416,1608 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 416/409, 1608/716?

Answer: GCF of Numerators as per given numbers 416/409, 1608/716 is

GCF of Numerators i.e. for 416,1608 is 8

LCM of denominators i.e. for 409,716 is 292844.

Thus, GCF of Fractions is 8/292844.Finally, GCF of Fractions for 416/409, 1608/716 is 8/292844.