How to Find GCF of 2224/375, 3670/778?

GCF of 2224/375, 3670/778

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 2224/375, 3670/778 i.e 2/291750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2224/375, 3670/778.

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 2224/375,3670/778?

Given fractions are 2224/375,3670/778

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 2224/375,3670/778, numerators are 2224,3670

Denominators are 375,778

The GCF of 2224,3670 is 2 .

LCM of 375,778 is 291750.

The greatest common factor of 2224/375,3670/778 = [GCF of 2224,3670]/[LCM of 375,778]= 2/291750

Therefore, the GCF of 2224/375,3670/778 is 2/291750.

Greatest Common Factor of 2224,3670

To find the highest common factor of 2224,3670, we have to find the factors of both numbers and list the highest common factor.

The factors of 2224 are 1, 2, 4, 8, 16, 139, 278, 556, 1112, 2224

The factors of 3670 are 1, 2, 5, 10, 367, 734, 1835, 3670

The HCF of 2224,3670 is 2.

Lets's calculate GCF of 2224,3670

Greatest Common Factor (GCF) of 2224,3670 By Common Division

2	2224, 3670
	1112, 1835

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

Greatest Common Factor of 2224,3670 By Matching Biggest Common Factor Method

Now, list down the factors of 2224

1,2,4,8,16,139,278,556,1112,2224

Now, list down the factors of 3670

1,2,5,10,367,734,1835,3670

Greatest Common Factor

We found the factors 2224,3670 . The biggest common factor number is the GCF number.
So the greatest common factor 2224,3670 is 2.

Lets's calculate LCM of 375,778

Lowest Common Multiple of 375,778 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 291750

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/291750

Therefore, the GCF of Fractions 2224/375,3670/778 is 2/291750

Least Common Multiple of 375,778 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 375,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(375,778) = 1

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

GCF(375,778) x common factors =1 x 1 = 1

LCM(375,778) = ( 375 × 778 ) / 1

LCM(375,778) = 291750 / 1

LCM(375,778) = 291750

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FAQs on GCF of Fractions of 2224/375, 3670/778

1. What is the HCF of 2224,3670?

The HCF of 2224,3670 is 2

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 2224/375, 3670/778?

Answer: GCF of Numerators as per given numbers 2224/375, 3670/778 is

GCF of Numerators i.e. for 2224,3670 is 2

LCM of denominators i.e. for 375,778 is 291750.

Thus, GCF of Fractions is 2/291750.Finally, GCF of Fractions for 2224/375, 3670/778 is 2/291750.