How to Find GCF of 105/600, 7370/682?

GCF of 105/600, 7370/682

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 105/600, 7370/682 i.e 5/204600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/600, 7370/682.

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 105/600,7370/682?

Given fractions are 105/600,7370/682

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 105/600,7370/682, numerators are 105,7370

Denominators are 600,682

The GCF of 105,7370 is 5 .

LCM of 600,682 is 204600.

The greatest common factor of 105/600,7370/682 = [GCF of 105,7370]/[LCM of 600,682]= 5/204600

Therefore, the GCF of 105/600,7370/682 is 5/204600.

Greatest Common Factor of 105,7370

To find the highest common factor of 105,7370, we have to find the factors of both numbers and list the highest common factor.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The factors of 7370 are 1, 2, 5, 10, 11, 22, 55, 67, 110, 134, 335, 670, 737, 1474, 3685, 7370

The HCF of 105,7370 is 5.

Lets's calculate GCF of 105,7370

Greatest Common Factor (GCF) of 105,7370 By Common Division

5	105, 7370
	21, 1474

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 105,7370 By Matching Biggest Common Factor Method

Now, list down the factors of 105

1,3,5,7,15,21,35,105

Now, list down the factors of 7370

1,2,5,10,11,22,55,67,110,134,335,670,737,1474,3685,7370

Greatest Common Factor

We found the factors 105,7370 . The biggest common factor number is the GCF number.
So the greatest common factor 105,7370 is 5.

Lets's calculate LCM of 600,682

Lowest Common Multiple of 600,682 using Common Division

2	600, 682
	300, 341

∴ So the LCM of the given numbers is 2 x 300 x 341 = 204600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/204600

Therefore, the GCF of Fractions 105/600,7370/682 is 5/204600

Least Common Multiple of 600,682 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 600,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(600,682) = 2

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

GCF(600,682) x common factors =2 x 1 = 2

LCM(600,682) = ( 600 × 682 ) / 2

LCM(600,682) = 409200 / 2

LCM(600,682) = 204600

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FAQs on GCF of Fractions of 105/600, 7370/682

1. What is the HCF of 105,7370?

The HCF of 105,7370 is 5

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 105/600, 7370/682?

Answer: GCF of Numerators as per given numbers 105/600, 7370/682 is

GCF of Numerators i.e. for 105,7370 is 5

LCM of denominators i.e. for 600,682 is 204600.

Thus, GCF of Fractions is 5/204600.Finally, GCF of Fractions for 105/600, 7370/682 is 5/204600.