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GCF of 219/400, 564/912

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 219/400, 564/912 i.e 3/22800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 219/400, 564/912.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 219/400,564/912?

Given fractions are 219/400,564/912

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 219/400,564/912, numerators are 219,564

Denominators are 400,912

The GCF of 219,564 is 3 .

LCM of 400,912 is 22800.

The greatest common factor of 219/400,564/912 = [GCF of 219,564]/[LCM of 400,912]= 3/22800

Therefore, the GCF of 219/400,564/912 is 3/22800.

Greatest Common Factor of 219,564

To find the highest common factor of 219,564, we have to find the factors of both numbers and list the highest common factor.

The factors of 219 are 1, 3, 73, 219

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

The HCF of 219,564 is 3.

Lets's calculate GCF of 219,564

Greatest Common Factor (GCF) of 219,564 By Common Division

3 219, 564
73, 188

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 219,564 By Matching Biggest Common Factor Method

Greatest Common Factor of 219,564 By Matching Biggest Common Factor Method

Now, list down the factors of 219

:

1,3,73,219

Now, list down the factors of 564

:

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

Greatest Common Factor

We found the factors 219,564 . The biggest common factor number is the GCF number.
So the greatest common factor 219,564 is 3.

Lets's calculate LCM of 400,912

Lowest Common Multiple of 400,912 using Common Division

2 400, 912
2 200, 456
2 100, 228
2 50, 114
25, 57

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 25 x 57 = 22800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22800

Therefore, the GCF of Fractions 219/400,564/912 is 3/22800

Least Common Multiple of 400,912 with GCF Formula

Least Common Multiple of 400,912 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 400,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,912) = 16

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

GCF(400,912) x common factors =16 x 1 = 16

LCM(400,912) = ( 400 × 912 ) / 16

LCM(400,912) = 364800 / 16

LCM(400,912) = 22800


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FAQs on GCF of Fractions of 219/400, 564/912

1. What is the HCF of 219,564?

The HCF of 219,564 is 3

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 219/400, 564/912?

Answer: GCF of Numerators as per given numbers 219/400, 564/912 is

GCF of Numerators i.e. for 219,564 is 3

LCM of denominators i.e. for 400,912 is 22800.

Thus, GCF of Fractions is 3/22800.Finally, GCF of Fractions for 219/400, 564/912 is 3/22800.