How to Find GCF of 68/414, 105/316, 941/758?

GCF of 68/414, 105/316, 941/758

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 68/414, 105/316, 941/758 i.e 1/24791148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/414, 105/316, 941/758.

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 68/414,105/316,941/758?

Given fractions are 68/414,105/316,941/758

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 68/414,105/316,941/758, numerators are 68,105,941

Denominators are 414,316,758

The GCF of 68,105,941 is 1 .

LCM of 414,316,758 is 24791148.

The greatest common factor of 68/414,105/316,941/758 = [GCF of 68,105,941]/[LCM of 414,316,758]= 1/24791148

Therefore, the GCF of 68/414,105/316,941/758 is 1/24791148.

Greatest Common Factor of 68,105,941

To find the highest common factor of 68,105,941, we have to find the factors of both numbers and list the highest common factor.

The factors of 68 are 1, 2, 4, 17, 34, 68

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

The factors of 941 are 1, 941

The HCF of 68,105,941 is 1.

Lets's calculate GCF of 68,105,941

Greatest Common Factor (GCF) of 68,105,941 By Common Division

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

Greatest Common Factor of 68,105,941 By Matching Biggest Common Factor Method

Now, list down the factors of 68

1,2,4,17,34,68

Now, list down the factors of 105

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

Now, list down the factors of 941

1,941

Greatest Common Factor

We found the factors 68,105,941 . The biggest common factor number is the GCF number.
So the greatest common factor 68,105,941 is 1.

Lets's calculate LCM of 414,316,758

Lowest Common Multiple of 414,316,758 using Common Division

2	414, 316, 758
	207, 158, 379

∴ So the LCM of the given numbers is 2 x 207 x 158 x 379 = 24791148

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24791148

Therefore, the GCF of Fractions 68/414,105/316,941/758 is 1/24791148

Least Common Multiple of 414,316,758 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 414,316,758 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,316,758) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(414,316,758) x common factors =2 x 2 = 4

LCM(414,316,758) = ( 414 × 316 × 758 ) / 4

LCM(414,316,758) = 99164592 / 4

LCM(414,316,758) = 24791148

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 68/414, 105/316, 941/758

1. What is the HCF of 68,105,941?

The HCF of 68,105,941 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 68/414, 105/316, 941/758?

Answer: GCF of Numerators as per given numbers 68/414, 105/316, 941/758 is

GCF of Numerators i.e. for 68,105,941 is 1

LCM of denominators i.e. for 414,316,758 is 24791148.

Thus, GCF of Fractions is 1/24791148.Finally, GCF of Fractions for 68/414, 105/316, 941/758 is 1/24791148.