How to Find GCF of 3045/456, 7221/692?

GCF of 3045/456, 7221/692

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 3045/456, 7221/692 i.e 87/78888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3045/456, 7221/692.

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 3045/456,7221/692?

Given fractions are 3045/456,7221/692

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 3045/456,7221/692, numerators are 3045,7221

Denominators are 456,692

The GCF of 3045,7221 is 87 .

LCM of 456,692 is 78888.

The greatest common factor of 3045/456,7221/692 = [GCF of 3045,7221]/[LCM of 456,692]= 87/78888

Therefore, the GCF of 3045/456,7221/692 is 87/78888.

Greatest Common Factor of 3045,7221

To find the highest common factor of 3045,7221, we have to find the factors of both numbers and list the highest common factor.

The factors of 3045 are 1, 3, 5, 7, 15, 21, 29, 35, 87, 105, 145, 203, 435, 609, 1015, 3045

The factors of 7221 are 1, 3, 29, 83, 87, 249, 2407, 7221

The HCF of 3045,7221 is 87.

Lets's calculate GCF of 3045,7221

Greatest Common Factor (GCF) of 3045,7221 By Common Division

3	3045, 7221
29	1015, 2407
	35, 83

∴ So the GCF of the given numbers is 3 x 29 = 87

Greatest Common Factor of 3045,7221 By Matching Biggest Common Factor Method

Now, list down the factors of 3045

1,3,5,7,15,21,29,35,87,105,145,203,435,609,1015,3045

Now, list down the factors of 7221

1,3,29,83,87,249,2407,7221

Greatest Common Factor

We found the factors 3045,7221 . The biggest common factor number is the GCF number.
So the greatest common factor 3045,7221 is 87.

Lets's calculate LCM of 456,692

Lowest Common Multiple of 456,692 using Common Division

2	456, 692
2	228, 346
	114, 173

∴ So the LCM of the given numbers is 2 x 2 x 114 x 173 = 78888

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 87/78888

Therefore, the GCF of Fractions 3045/456,7221/692 is 87/78888

Least Common Multiple of 456,692 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 456,692 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(456,692) = 4

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

GCF(456,692) x common factors =4 x 1 = 4

LCM(456,692) = ( 456 × 692 ) / 4

LCM(456,692) = 315552 / 4

LCM(456,692) = 78888

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FAQs on GCF of Fractions of 3045/456, 7221/692

1. What is the HCF of 3045,7221?

The HCF of 3045,7221 is 87

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 3045/456, 7221/692?

Answer: GCF of Numerators as per given numbers 3045/456, 7221/692 is

GCF of Numerators i.e. for 3045,7221 is 87

LCM of denominators i.e. for 456,692 is 78888.

Thus, GCF of Fractions is 87/78888.Finally, GCF of Fractions for 3045/456, 7221/692 is 87/78888.