How to Find GCF of 37/224, 3408/1008?

GCF of 37/224, 3408/1008

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 37/224, 3408/1008 i.e 1/2016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 37/224, 3408/1008.

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 37/224,3408/1008?

Given fractions are 37/224,3408/1008

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 37/224,3408/1008, numerators are 37,3408

Denominators are 224,1008

The GCF of 37,3408 is 1 .

LCM of 224,1008 is 2016.

The greatest common factor of 37/224,3408/1008 = [GCF of 37,3408]/[LCM of 224,1008]= 1/2016

Therefore, the GCF of 37/224,3408/1008 is 1/2016.

Greatest Common Factor of 37,3408

To find the highest common factor of 37,3408, we have to find the factors of both numbers and list the highest common factor.

The factors of 37 are 1, 37

The factors of 3408 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 71, 142, 213, 284, 426, 568, 852, 1136, 1704, 3408

The HCF of 37,3408 is 1.

Lets's calculate GCF of 37,3408

Greatest Common Factor (GCF) of 37,3408 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 37,3408 By Matching Biggest Common Factor Method

Now, list down the factors of 37

1,37

Now, list down the factors of 3408

1,2,3,4,6,8,12,16,24,48,71,142,213,284,426,568,852,1136,1704,3408

Greatest Common Factor

We found the factors 37,3408 . The biggest common factor number is the GCF number.
So the greatest common factor 37,3408 is 1.

Lets's calculate LCM of 224,1008

Lowest Common Multiple of 224,1008 using Common Division

2	224, 1008
2	112, 504
2	56, 252
2	28, 126
7	14, 63
	2, 9

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 7 x 2 x 9 = 2016

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2016

Therefore, the GCF of Fractions 37/224,3408/1008 is 1/2016

Least Common Multiple of 224,1008 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 224,1008 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(224,1008) = 112

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

GCF(224,1008) x common factors =112 x 1 = 112

LCM(224,1008) = ( 224 × 1008 ) / 112

LCM(224,1008) = 225792 / 112

LCM(224,1008) = 2016

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FAQs on GCF of Fractions of 37/224, 3408/1008

1. What is the HCF of 37,3408?

The HCF of 37,3408 is 1

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 37/224, 3408/1008?

Answer: GCF of Numerators as per given numbers 37/224, 3408/1008 is

GCF of Numerators i.e. for 37,3408 is 1

LCM of denominators i.e. for 224,1008 is 2016.

Thus, GCF of Fractions is 1/2016.Finally, GCF of Fractions for 37/224, 3408/1008 is 1/2016.