How to Find GCF of 7678/398, 8273/300?

GCF of 7678/398, 8273/300

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 7678/398, 8273/300 i.e 1/59700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7678/398, 8273/300.

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 7678/398,8273/300?

Given fractions are 7678/398,8273/300

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 7678/398,8273/300, numerators are 7678,8273

Denominators are 398,300

The GCF of 7678,8273 is 1 .

LCM of 398,300 is 59700.

The greatest common factor of 7678/398,8273/300 = [GCF of 7678,8273]/[LCM of 398,300]= 1/59700

Therefore, the GCF of 7678/398,8273/300 is 1/59700.

Greatest Common Factor of 7678,8273

To find the highest common factor of 7678,8273, we have to find the factors of both numbers and list the highest common factor.

The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678

The factors of 8273 are 1, 8273

The HCF of 7678,8273 is 1.

Lets's calculate GCF of 7678,8273

Greatest Common Factor (GCF) of 7678,8273 By Common Division

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

Greatest Common Factor of 7678,8273 By Matching Biggest Common Factor Method

Now, list down the factors of 7678

1,2,11,22,349,698,3839,7678

Now, list down the factors of 8273

1,8273

Greatest Common Factor

We found the factors 7678,8273 . The biggest common factor number is the GCF number.
So the greatest common factor 7678,8273 is 1.

Lets's calculate LCM of 398,300

Lowest Common Multiple of 398,300 using Common Division

2	398, 300
	199, 150

∴ So the LCM of the given numbers is 2 x 199 x 150 = 59700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59700

Therefore, the GCF of Fractions 7678/398,8273/300 is 1/59700

Least Common Multiple of 398,300 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 398,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(398,300) = 2

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

GCF(398,300) x common factors =2 x 1 = 2

LCM(398,300) = ( 398 × 300 ) / 2

LCM(398,300) = 119400 / 2

LCM(398,300) = 59700

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FAQs on GCF of Fractions of 7678/398, 8273/300

1. What is the HCF of 7678,8273?

The HCF of 7678,8273 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 7678/398, 8273/300?

Answer: GCF of Numerators as per given numbers 7678/398, 8273/300 is

GCF of Numerators i.e. for 7678,8273 is 1

LCM of denominators i.e. for 398,300 is 59700.

Thus, GCF of Fractions is 1/59700.Finally, GCF of Fractions for 7678/398, 8273/300 is 1/59700.