How to Find GCF of 69/10, 40/963, 105/669?

GCF of 69/10, 40/963, 105/669

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 69/10, 40/963, 105/669 i.e 1/2147490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/10, 40/963, 105/669.

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 69/10,40/963,105/669?

Given fractions are 69/10,40/963,105/669

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 69/10,40/963,105/669, numerators are 69,40,105

Denominators are 10,963,669

The GCF of 69,40,105 is 1 .

LCM of 10,963,669 is 2147490.

The greatest common factor of 69/10,40/963,105/669 = [GCF of 69,40,105]/[LCM of 10,963,669]= 1/2147490

Therefore, the GCF of 69/10,40/963,105/669 is 1/2147490.

Greatest Common Factor of 69,40,105

To find the highest common factor of 69,40,105, we have to find the factors of both numbers and list the highest common factor.

The factors of 69 are 1, 3, 23, 69

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

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

The HCF of 69,40,105 is 1.

Lets's calculate GCF of 69,40,105

Greatest Common Factor (GCF) of 69,40,105 By Common Division

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

Greatest Common Factor of 69,40,105 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 105

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

Greatest Common Factor

We found the factors 69,40,105 . The biggest common factor number is the GCF number.
So the greatest common factor 69,40,105 is 1.

Lets's calculate LCM of 10,963,669

Lowest Common Multiple of 10,963,669 using Common Division

3	10, 963, 669
	10, 321, 223

∴ So the LCM of the given numbers is 3 x 10 x 321 x 223 = 2147490

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2147490

Therefore, the GCF of Fractions 69/10,40/963,105/669 is 1/2147490

Least Common Multiple of 10,963,669 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 10,963,669 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(10,963,669) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(10,963,669) x common factors =1 x 3 = 3

LCM(10,963,669) = ( 10 × 963 × 669 ) / 3

LCM(10,963,669) = 6442470 / 3

LCM(10,963,669) = 2147490

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 69/10, 40/963, 105/669

1. What is the HCF of 69,40,105?

The HCF of 69,40,105 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 69/10, 40/963, 105/669?

Answer: GCF of Numerators as per given numbers 69/10, 40/963, 105/669 is

GCF of Numerators i.e. for 69,40,105 is 1

LCM of denominators i.e. for 10,963,669 is 2147490.

Thus, GCF of Fractions is 1/2147490.Finally, GCF of Fractions for 69/10, 40/963, 105/669 is 1/2147490.