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GCF of 224/656, 412/112

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 224/656, 412/112 i.e 4/4592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/656, 412/112.

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 224/656,412/112?

Given fractions are 224/656,412/112

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 224/656,412/112, numerators are 224,412

Denominators are 656,112

The GCF of 224,412 is 4 .

LCM of 656,112 is 4592.

The greatest common factor of 224/656,412/112 = [GCF of 224,412]/[LCM of 656,112]= 4/4592

Therefore, the GCF of 224/656,412/112 is 4/4592.

Greatest Common Factor of 224,412

To find the highest common factor of 224,412, we have to find the factors of both numbers and list the highest common factor.

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

The factors of 412 are 1, 2, 4, 103, 206, 412

The HCF of 224,412 is 4.

Lets's calculate GCF of 224,412

Greatest Common Factor (GCF) of 224,412 By Common Division

2 224, 412
2 112, 206
56, 103

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

Greatest Common Factor of 224,412 By Matching Biggest Common Factor Method

Greatest Common Factor of 224,412 By Matching Biggest Common Factor Method

Now, list down the factors of 224

:

1,2,4,7,8,14,16,28,32,56,112,224

Now, list down the factors of 412

:

1,2,4,103,206,412

Greatest Common Factor

We found the factors 224,412 . The biggest common factor number is the GCF number.
So the greatest common factor 224,412 is 4.

Lets's calculate LCM of 656,112

Lowest Common Multiple of 656,112 using Common Division

2 656, 112
2 328, 56
2 164, 28
2 82, 14
41, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 41 x 7 = 4592

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/4592

Therefore, the GCF of Fractions 224/656,412/112 is 4/4592

Least Common Multiple of 656,112 with GCF Formula

Least Common Multiple of 656,112 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 656,112 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(656,112) = 16

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

GCF(656,112) x common factors =16 x 1 = 16

LCM(656,112) = ( 656 × 112 ) / 16

LCM(656,112) = 73472 / 16

LCM(656,112) = 4592


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FAQs on GCF of Fractions of 224/656, 412/112

1. What is the HCF of 224,412?

The HCF of 224,412 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 224/656, 412/112?

Answer: GCF of Numerators as per given numbers 224/656, 412/112 is

GCF of Numerators i.e. for 224,412 is 4

LCM of denominators i.e. for 656,112 is 4592.

Thus, GCF of Fractions is 4/4592.Finally, GCF of Fractions for 224/656, 412/112 is 4/4592.