How to Find GCF of 564/299, 416/486?

GCF of 564/299, 416/486

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 564/299, 416/486 i.e 4/145314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/299, 416/486.

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 564/299,416/486?

Given fractions are 564/299,416/486

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 564/299,416/486, numerators are 564,416

Denominators are 299,486

The GCF of 564,416 is 4 .

LCM of 299,486 is 145314.

The greatest common factor of 564/299,416/486 = [GCF of 564,416]/[LCM of 299,486]= 4/145314

Therefore, the GCF of 564/299,416/486 is 4/145314.

Greatest Common Factor of 564,416

To find the highest common factor of 564,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

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

The HCF of 564,416 is 4.

Lets's calculate GCF of 564,416

Greatest Common Factor (GCF) of 564,416 By Common Division

2	564, 416
2	282, 208
	141, 104

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

Greatest Common Factor of 564,416 By Matching Biggest Common Factor Method

Now, list down the factors of 564

1,2,3,4,6,12,47,94,141,188,282,564

Now, list down the factors of 416

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

Greatest Common Factor

We found the factors 564,416 . The biggest common factor number is the GCF number.
So the greatest common factor 564,416 is 4.

Lets's calculate LCM of 299,486

Lowest Common Multiple of 299,486 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 145314

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/145314

Therefore, the GCF of Fractions 564/299,416/486 is 4/145314

Least Common Multiple of 299,486 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 299,486 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(299,486) = 1

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

GCF(299,486) x common factors =1 x 1 = 1

LCM(299,486) = ( 299 × 486 ) / 1

LCM(299,486) = 145314 / 1

LCM(299,486) = 145314

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FAQs on GCF of Fractions of 564/299, 416/486

1. What is the HCF of 564,416?

The HCF of 564,416 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 564/299, 416/486?

Answer: GCF of Numerators as per given numbers 564/299, 416/486 is

GCF of Numerators i.e. for 564,416 is 4

LCM of denominators i.e. for 299,486 is 145314.

Thus, GCF of Fractions is 4/145314.Finally, GCF of Fractions for 564/299, 416/486 is 4/145314.