How to Find GCF of 7852/768, 9682/9224?

GCF of 7852/768, 9682/9224

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 7852/768, 9682/9224 i.e 2/885504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7852/768, 9682/9224.

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 7852/768,9682/9224?

Given fractions are 7852/768,9682/9224

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 7852/768,9682/9224, numerators are 7852,9682

Denominators are 768,9224

The GCF of 7852,9682 is 2 .

LCM of 768,9224 is 885504.

The greatest common factor of 7852/768,9682/9224 = [GCF of 7852,9682]/[LCM of 768,9224]= 2/885504

Therefore, the GCF of 7852/768,9682/9224 is 2/885504.

Greatest Common Factor of 7852,9682

To find the highest common factor of 7852,9682, we have to find the factors of both numbers and list the highest common factor.

The factors of 7852 are 1, 2, 4, 13, 26, 52, 151, 302, 604, 1963, 3926, 7852

The factors of 9682 are 1, 2, 47, 94, 103, 206, 4841, 9682

The HCF of 7852,9682 is 2.

Lets's calculate GCF of 7852,9682

Greatest Common Factor (GCF) of 7852,9682 By Common Division

2	7852, 9682
	3926, 4841

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

Greatest Common Factor of 7852,9682 By Matching Biggest Common Factor Method

Now, list down the factors of 7852

1,2,4,13,26,52,151,302,604,1963,3926,7852

Now, list down the factors of 9682

1,2,47,94,103,206,4841,9682

Greatest Common Factor

We found the factors 7852,9682 . The biggest common factor number is the GCF number.
So the greatest common factor 7852,9682 is 2.

Lets's calculate LCM of 768,9224

Lowest Common Multiple of 768,9224 using Common Division

2	768, 9224
2	384, 4612
2	192, 2306
	96, 1153

∴ So the LCM of the given numbers is 2 x 2 x 2 x 96 x 1153 = 885504

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/885504

Therefore, the GCF of Fractions 7852/768,9682/9224 is 2/885504

Least Common Multiple of 768,9224 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 768,9224 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(768,9224) = 8

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

GCF(768,9224) x common factors =8 x 1 = 8

LCM(768,9224) = ( 768 × 9224 ) / 8

LCM(768,9224) = 7084032 / 8

LCM(768,9224) = 885504

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FAQs on GCF of Fractions of 7852/768, 9682/9224

1. What is the HCF of 7852,9682?

The HCF of 7852,9682 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 7852/768, 9682/9224?

Answer: GCF of Numerators as per given numbers 7852/768, 9682/9224 is

GCF of Numerators i.e. for 7852,9682 is 2

LCM of denominators i.e. for 768,9224 is 885504.

Thus, GCF of Fractions is 2/885504.Finally, GCF of Fractions for 7852/768, 9682/9224 is 2/885504.