How to Find GCF of 1732/614, 8814/443?

GCF of 1732/614, 8814/443

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 1732/614, 8814/443 i.e 2/272002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1732/614, 8814/443.

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 1732/614,8814/443?

Given fractions are 1732/614,8814/443

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 1732/614,8814/443, numerators are 1732,8814

Denominators are 614,443

The GCF of 1732,8814 is 2 .

LCM of 614,443 is 272002.

The greatest common factor of 1732/614,8814/443 = [GCF of 1732,8814]/[LCM of 614,443]= 2/272002

Therefore, the GCF of 1732/614,8814/443 is 2/272002.

Greatest Common Factor of 1732,8814

To find the highest common factor of 1732,8814, we have to find the factors of both numbers and list the highest common factor.

The factors of 1732 are 1, 2, 4, 433, 866, 1732

The factors of 8814 are 1, 2, 3, 6, 13, 26, 39, 78, 113, 226, 339, 678, 1469, 2938, 4407, 8814

The HCF of 1732,8814 is 2.

Lets's calculate GCF of 1732,8814

Greatest Common Factor (GCF) of 1732,8814 By Common Division

2	1732, 8814
	866, 4407

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

Greatest Common Factor of 1732,8814 By Matching Biggest Common Factor Method

Now, list down the factors of 1732

1,2,4,433,866,1732

Now, list down the factors of 8814

1,2,3,6,13,26,39,78,113,226,339,678,1469,2938,4407,8814

Greatest Common Factor

We found the factors 1732,8814 . The biggest common factor number is the GCF number.
So the greatest common factor 1732,8814 is 2.

Lets's calculate LCM of 614,443

Lowest Common Multiple of 614,443 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 272002

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/272002

Therefore, the GCF of Fractions 1732/614,8814/443 is 2/272002

Least Common Multiple of 614,443 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 614,443 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,443) = 1

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

GCF(614,443) x common factors =1 x 1 = 1

LCM(614,443) = ( 614 × 443 ) / 1

LCM(614,443) = 272002 / 1

LCM(614,443) = 272002

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FAQs on GCF of Fractions of 1732/614, 8814/443

1. What is the HCF of 1732,8814?

The HCF of 1732,8814 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 1732/614, 8814/443?

Answer: GCF of Numerators as per given numbers 1732/614, 8814/443 is

GCF of Numerators i.e. for 1732,8814 is 2

LCM of denominators i.e. for 614,443 is 272002.

Thus, GCF of Fractions is 2/272002.Finally, GCF of Fractions for 1732/614, 8814/443 is 2/272002.